SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.


 Phyllis Goodman
 3 years ago
 Views:
Transcription
1 Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective rate that corresponds to a nominal rate of 20% compounded quarterly? 2) How many years will it take for a principal to double at a rate of 10% compounded annually? Give your answer to the nearest year. 3) To what sum will $1000 accumulate if it is invested at 10% compounded annually for one year and then at 10% compounded semiannually for two years? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) An interest rate of 8% compounded semiannually corresponds to an effective rate of A) 8%. B) %. C) %. D) %. E) 12%. 5) A trust fund is to be established by a single payment so that at the end of 15 years, there will be $20,000 in the fund. If the fund earns interest at the rate of 8% compounded semiannually, how much should be deposited initially into the fund? A) $ B) $ C) $ D) $ E) $11, SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) Find the effective rate that corresponds to an interest rate of 5% compounded daily. 7) Over a period of 3 years, an original principal of $1000 accumulated to $1200 in an account where the interest rate was compounded monthly. Determine the rate of interest to two decimal places. 8) At what nominal rate of interest, compounded quarterly, will money double in 10 years? 9) If an initial investment of $4000 grows to $4884 in five years, find the nominal rate of interest, compounded monthly, that was earned by the money. 10) If an initial investment of $4000 grows to $5718 in six years, find the nominal rate of interest, compounded quarterly, that was earned by the money. 11) If an initial investment of $3000 grows to $18,000 in ten years, find the nominal rate of interest, compounded monthly, that was earned by the money. 12) If an initial investment of $3000 grows to $18,000 in five years, find the nominal rate of interest, compounded quarterly, that was earned by the money. 13) Suppose you leave an initial amount of $315 in a savings account for 10 years. If interest is compounded monthly, use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest. Determine the nominal rate of interest so that there is $519 after 10 years. Page 200
2 14) At what nominal rate of interest, compounded monthly, will an investment double in 15 years? 15) At what nominal rate of interest, compounded quarterly, will an investment double in 15 years? 16) At what nominal rate of interest, compounded semiannually, will an investment double in 20 years? 17) At what nominal rate of interest, compounded monthly, will an investment triple in 20 years? 18) Suppose you leave an initial amount of $250 in a savings account for 20 years. If interest is compounded daily (use 365 times per year), use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest. Determine the nominal rate of interest so that the amount doubles after 20 years. 19) Suppose you leave an initial amount of $320 in a savings account for 30 years. If interest is compounded monthly, use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest. Determine the nominal rate of interest so that the amount triples after 30 years. 20) An initial investment of $2600 grows at an annual rate of 7.5% compounded monthly. Find how long it takes for the investment to amount to $ ) An initial investment of $300 grows at an annual rate of 4.5% compounded bimonthly. Find how long it takes for the investment to amount to $ ) An initial investment of $240 grows at an annual rate of 5% compounded quarterly. Find how long it takes for the investment to amount to $ ) An initial investment of $10,000 grows at an annual rate of 3.5% compounded monthly. Find how long it takes for the investment to amount to $14, ) Suppose you invest an initial amount of $10,000 at an annual rate of 8.2% compounded monthly. Use a graphing calculator to graph the compound amount S as a function of the interest periods. Determine how long it takes for the investment to accumulate to $22, ) Suppose an initial investment grows from $2000 to $ over three years. First find the nominal rate compounded monthly and then find the equivalent effective rate. 26) Suppose an initial investment grows from $330 to $600 over five years. First find the nominal rate compounded monthly and then find the equivalent effective rate. 27) Suppose an initial investment grows from $12,000 to $30,000 over ten years. First find the nominal rate compounded quarterly and then find the equivalent effective rate. 28) Suppose an initial investment grows from $220 to $600 over fifteen years. First find the nominal rate compounded monthly and then find the equivalent effective rate. 29) An investment is compounded daily (use 365 times per year). Use a graphing calculator to graph the effective rate, re, as a function of the nominal rate r. Then use the graph to find the nominal rate that is equivalent to an effective rate of 5.4%. Page 201
3 30) The population of a small town is growing at an effective rate of 2.1%. If the current population is 53,000, what will the population be in 8 years? 31) An investment is growing at an effective rate of 12.4%. If the amount invested is currently $12,000, what will the amount be in 6 years? 32) A house worth $150,000 ten years ago has increased in value at an effective rate of 3% due to inflation. Find the current value of the home. 33) A $6000 investment in a stock five years ago grew at an effective rate of 19.6%. Find the current value of the investment. 34) An investment grows from $600 to $642 in one year. If the investment continues to grow at that rate, find the number of years it will take for the investment to double. 35) An investment grows from $10,240 to $10, in one year. If the investment continues to grow at that rate, find the number of years it will take the investment to double. 36) The population of a city grows from 110,000 to 116,600 in one year. If the city continues to grow at that rate, find the number of years it will take for the population to double. 37) An investment grows from $5500 to $6105 in one year. If the investment continues to grow at that rate, find the number of years it will take for the investment to triple. 38) Suppose you can invest $10,000 at 4.5% compounded quarterly or at 4.7% compounded annually. Which is the better choice and how much more per year would you earn? 39) Suppose you can invest $6000 at 6.2% compounded monthly or at 6.5% compounded semiannually. Which is the better choice and how much more per year would you earn? 40) You have a choice of two banks. One bank pays interest at 4.66% compounded 360 times a year and the other bank pays interest at 4.65% compounded 365 times a year. Which is the better choice? 41) You have a choice of two banks. One bank pays interest at 5.54% compounded monthly and the other bank pays interest at 5.53% compounded daily (365 times a year). Which is the better choice? How much more would you make in one year if you deposited $1000? 42) You have two investment opportunities. You can invest $6000 at 12% compounded monthly or you can invest $6100 at 12.1% compounded quarterly. Which has the better effective rate of interest? Use a graphing calculator to graph both amounts as a function of time in years. Which is the better investment over twenty years? 43) If $1,000 is invested at a nominal rate of 4% compounded quarterly for 5 years, find the compound amount. 44) If $2,575 is invested at an A.P.R. of 7% compounded semiannually for 15 years, find the accumulated amount. 45) If $4,200 is invested at an annual rate of 5.4% compounded monthly for 10 years, find the compound amount. Page 202
4 46) If $3,100 is invested at a nominal rate of 6% compounded quarterly for 7 years, find a) the compound amount, and b) the compound interest. 47) If $14,300 is invested at an A.P.R. of 8.25% compounded semiannually for 3 years, find a) the compound amount, and b) the compound interest. 48) If $10,000 is invested at an effective rate of 4.25% for 8 years, what is the accumulated amount? 49) If $5,600 is invested at an effective rate of 2.1% for 17 years, what is the compound amount? 5.2 Present Value SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Determine the present value of $4000 due in 5 years if the interest rate is 10% compounded semiannually. 2) A debt of $2000 due four years from now is to be repaid by a payment of $1000 now and a second payment at the end of two years. How much should the second payment be if the interest rate is 5% compounded annually? 3) A person has the option of satisfying a debt by either paying $5000 now and $5000 in two years, or by paying $3000 now, $3000 a year from now, and a final payment of x dollars two years from now. Determine an equation of value that corresponds to the value of all payments at the end of two years. It is not necessary to solve the equation. Assume that interest is at the rate of 10% compounded semiannually. 4) For an initial investment of $10,000, suppose a company guarantees the following cash flows at the end of the indicated years: Year Cash Flow 1 $ $8000 Assume an interest rate of 5% compounded annually. (a) Determine the net present value of the cash flows. (b) Is the investment profitable? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5) A debt of $2000 due in one year is to be repaid by a payment due two years from now and a final payment of $1000 three years from now. If the interest is at the rate of 4% compounded annually, then the payment due in two years is A) $ B) $ C) $ D) $ E) $ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) To purchase land for an industrial site, a company agrees to pay $20,000 down and $10,000 at the end of every sixmonth period for 10 years. If the interest rate is 10% compounded semiannually, what is the corresponding cash value of the land? 7) Find the present value of $5000 due in 3 years if the interest rate is 6 3 % compounded monthly. 4 Page 203
5 8) A bank pays 4% annual interest compounded quarterly. How large a deposit must be made now in order that the account contains $1500 at the end of 3 years? 9) Find the present value of $3000 due after five years if the interest rate is 9.6% compounded semiannually. 10) Find the present value of $300 due after six years if the interest rate is 5.4% compounded monthly. 11) How much must be invested at an interest rate of 7.25% compounded quarterly to have $10,000 in two years? 12) How much must be invested at an interest rate of 9.6% compounded monthly to have $3000 in five years? 13) A trust fund for a childʹs education is being set up by a single payment so that at the end of 17 years there will be $31,000. If the fund earns interest at the rate of 8.25% compounded monthly, how much money should be paid into the fund initially? 14) A trust fund for a 12yearold child is being set up by a single payment so that when the child is 21 there will be $24,000. If the fund earns interest at the rate of 7.25% compounded quarterly, how much money should be paid into the fund initially? 15) A trust fund for a newborn is being set up by a single payment so that at the end of 18 years there will be $34,000. If the fund earns interest at the rate of 6.25% compounded monthly, how much money should be paid into the fund initially? 16) A trust fund for a 8yearold child is being set up by a single payment so that when the child is 20 there will be $12,000. If the fund earns interest at the rate of 6.5% compounded semiannually, how much money should be paid into the fund initially? 17) A debt of $12,000, which is due 10 years from now, is instead to be paid off by four payments: $3000 now, $2000 in 3 years, $2000 in 6 years, and a final payment at the end of 8 years. What would this payment be if an interest rate of 5.5% compounded semiannually is assumed? 18) Suppose Mr. Takegawa owes Ms. Perez three sums of money: $1000 due in 2 years, $1500 due in 5 years, and $2000 due in 8 years. Suppose he would rather pay her $2000 now and the rest in 3 years. If the interest rate is 6% compounded annually, how much will he owe in 3 years? 19) A debt of $600 is due 3 years from now and $800 due 5 years from now, is instead to be paid off by two payments: $500 now and a final payment at the end of 6 years. What would this payment be if an interest rate of 6% compounded quarterly is assumed? 20) A debt of $1000 due 4 years from now and $1500 due 6 years from now, is instead to be paid off by a single payment 5 years from now. How much is the payment if an interest rate of 8.4% compounded monthly is assumed? 21) Miguel has the opportunity to invest $3000 in a friendʹs business such that he will be repaid $4500 in six years. On the other hand, he can put the $3000 in a savings account that pays 5.5% compounded quarterly. Which investment is better? Page 204
6 22) Miguel has the opportunity to invest $3000 in a friendʹs business such that he will be repaid $4500 in six years. If he instead wanted to put the $3000 into a savings account, what interest rate compounded monthly would be needed to equal the investment? 23) Suppose you have the opportunity to invest $6000 in a business venture such that you will be repaid $8000 in five years. On the other hand, you can put the $6000 in a savings account that pays 5.25% compounded monthly. Which investment is better? 24) Suppose you have the opportunity to invest $1000 in a business such that the value of your investment after seven years will be $1500. On the other hand, you can put the $1000 into a certificate of deposit that pays 6% compounded monthly. Which is better? 25) Suppose that you can invest $10,000 in a business that guarantees you the following cash flows: $5000 at the end of 2 years, $4000 at the end of 4 years, and $3000 at the end of 6 years. Assuming an interest rate of 7.25% compounded annually, find the net present value of the cash flows. Is the investment profitable? 26) Suppose that you can invest $11,000 in a business that guarantees you the following cash flows: $5500 at the end of 2 years, $4500 at the end of 4 years, and $4000 at the end of 5 years. Assuming an interest rate of 6.25% compounded annually, find the net present value of the cash flows. Is the investment profitable? 27) Suppose that Tori can invest $13,000 in a business that guarantees her the following cash flows: $6000 at the end of 2 years, $5000 at the end of 4 years, and $4000 at the end of 6 years. Assuming an interest rate of 6% compounded monthly, find the present value of the cash flows. Is the investment profitable? 28) Suppose that you can invest $5000 in a business that guarantees you the following cash flows: $3000 at the end of 2 years, $2000 at the end of 4 years, and $2000 at the end of 6 years. Assuming an interest rate of 6% compounded monthly, find the present value of the cash flows. Is the investment profitable? 29) Suppose that you can invest $5000 in a business that guarantees you the following cash flows: $3000 at the end of 2 years, $2000 at the end of 4 years, and $1500 at the end of 6 years. Use a graphing calculator to graph the net present value as a function of the interest rate compounded annually. Determine the interest rate for which the investment is profitable. 30) Suppose that you can invest $8000 in a business that guarantees you the following cash flows: $4000 at the end of 2 years, $3500 at the end of 4 years, and $2000 at the end of 7 years. Use a graphing calculator to graph the net present value as a function of the interest rate compounded annually. Determine the interest rates for which the investment is profitable. 31) Find the present value of a future value of $5,000 due in 7 years at a nominal rate of 3% compounded quarterly. 32) Find the present value of a future value of $325 due in 10 years at an A.P.R. of 5.3% compounded semiannually. 33) Find the present value of a future value of $4,200 due in 11 years at a nominal rate of 6% compounded monthly. 34) Find the present value of a future value of $1,750 due in 9 years at an effective rate of 3.65%. 35) Find the present value of a future value of $4,650 due in 18 months at an effective rate of 4.55%. Page 205
7 5.3 Interest Compounded Continuously SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) If $1000 is deposited into a savings account that earns interest at an annual rate of 6% compounded continuously, find the value of the account at the end of seven years. Give your answer to the nearest dollar. 2) If $200 is deposited into a savings account that earns interest at an annual rate of 8% compounded continuously, find the value of the account at the end of two years. 3) Determine the effective rate equivalent to an annual rate of 8% compounded continuously. 4) Determine the effective rate equivalent to an annual rate of 10% compounded continuously. 5) At an annual rate of 4% compounded continuously, in how many years would it take for a principal to double? 6) At an annual rate of 8% compounded continuously, in how many years would it take for a principal to double? 7) In five years a company will purchase equipment costing $100,000. The company decides to place a single deposit into a savings account now so that its future value will equal the cost of the equipment. If the account earns interest at an annual rate of 10% compounded continuously, determine the deposit to the nearest dollar. 8) A trust fund is to be set up by a single payment so that at the end of 10 years there will be $1,000,000 in the fund. If interest is compounded continuously at an annual rate of 9%, to the nearest dollar, how much money should be paid into the fund initially? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 9) If an investment of $20,000 earns interest at an annual rate of 9% compounded continuously, then the value (in dollars) of the investment six years from now is A) 20,000(1.09)6 B) 20,000(1.09)6 C) 20,000e0.54 D) 20,000e0.54 e0.54 E) 20,000 10) If an investment of $12,000 earns interest at an annual rate of 7% compounded continuously, then the value (in dollars) of the investment ten years from now is A) 12,000(1.07)10 B) 12,000(1.07)10 C) 12, D) 12,000e0.7 e0.7 E) 12,000 Page 206
8 11) If money earns interest at an annual rate of 8% compounded continuously, then the value (in dollars) of $10,000 due at the end of five years is A) 10,000e0.4 B) 10,000e0.4 e0.4 C) 10,000 D) 10,000(1.08)5 E) 10,000(1.08)5 12) At an annual rate of 10% compounded continuously, the number of years in which a principal triples is A) ln ln B). C). D) 0.10 ln 3 3 ln E) e SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) Determine the effective rate equivalent to an annual rate of 7 3 % compounded continuously. 4 14) Given that the effective rate is 9%, determine the interest rate r which is compounded continuously to give an effective rate of 9%. 15) If a person deposits $1000 in a savings account that pays an interest rate of r% compounded continuously, and the account has $1400 at the end of 4 years, find the interest rate. 16) A person deposits $1000 in a savings account that pays an interest rate of 4 3 % compounded continuously. 4 Find the balance in the account at the end of years. 17) If $100 is invested at a rate of 5% compounded continuously, the amount in the account is given by: S = 100e0.05t. If the same principal is invested at an account earning 5% compounded semiannually, the amount is given by: S = x. Consider the difference in these two investments by graphing both functions on your graphing calculator and looking at the years 5 through 7. (Use the window 5, 7 128,142.) What do you notice about the two graphs? 18) If $100 is invested at a rate of 6% compounded continuously, the amount in the account is given by: S = 100e0.06t. If the principal is invested at an account earning 6% compounded monthly, the amount is given by: S = x. Consider the difference in these two investments by graphing both functions on your graphing calculator and looking at the years 5 through 6. (Use the window 5, 6 135,141.) What do you notice about the two graphs? 19) The function that gives the effective rate that corresponds to an annual rate of x interest compounded continuously is y = ex  1. Graph this on your graphing calculator in the window 0,0.5 0,1 and discuss what the behavior means. Page 207
9 20) Suppose that you want to invest some money in order to have $100 available at some later time. If you invest it at 7% interest compounded continuously, the amount you need to invest now, P, is related to the number of years from now that you need the money, t, by: P(t) = 100e0.07t. Graph this on your graphing calculator in the window 0,20 0,100 Discuss the behavior of this graph. 21) Suppose that you want to invest some money in order to have $1000 available at some later time. If you invest it at 7% interest compounded continuously, the amount you need to invest now, P, is related to the number of years from now that you need the money, t, by: P(t) = 1000e0.07t. Graph this on your graphing calculator in the window 0,20 0,1000. Discuss the behavior of this graph. 5.4 Annuities MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the first five terms of the geometric sequence. 1) a1 = 4, r = 2 A) 4, 8, 16, 32, 64 B) 8, 16, 32, 64, 128 C) 4, 6, 8, 10, 12 D) 2, 8, 32, 128, 512 2) a1 = 5, r = 1 4 A) 5, 5 4, 5 16, 5 64, C) 5 4, 5 16, 5 64, 5 256, B) 5, 20, 80, 320, 1280 D) 5, 21 4, 11 2, 23 4, 6 3) a1 = 7, r = 3 A) 7, 21, 63, 189, 567 B) 7, 21, 63, 189, 567 C) 3, 21, 63, 189, 567 D) 7, 4, 1, 2, 5 Find the value. a 4) A) B) C) D) ) a A) B) C) D) ) a A) B) C) D) ) s A) B) C) D) Page 208
10 8) s A) B) C) D) ) s A) B) C) D) ) s A) B) C) D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 11) Suppose a person deposits $1000 in a savings account at the end of every six months. What is the value of the account at the end of five years if interest is at a rate of 10% compounded semiannually? 12) To purchase land for an industrial site, a company agrees to pay $20,000 down and $10,000 at the end of every sixmonth period for 10 years. If the interest rate is 10% compounded semiannually, what is the corresponding cash value of the land? 13) A person establishes the following retirement plan: an immediate deposit of $10,000 and quarterly payments of $1,500 at the end of each quarter into a savings account that earns 5% compounded quarterly, what is the amount of the investment after 21 years? 14) Suppose an annuity due consists of 6 yearly payments of $200 and the interest rate is 5% compounded annually. Determine (a) the present value and (b) the future value at the end of 6 years. 15) Suppose a corporation pays $50,000 for a machine that has a useful life of eight years and a salvage value of $5000. A sinking fund is established to replace the machine at the end of 8 years. The replacement machine will cost $70,000. If equal payments are made into the fund at the end of every 6 months and the fund earns interest at the rate of 10% compounded semiannually, what should each payment be? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 16) Suppose $500 is initially placed in a savings account that earns interest at the rate of 8% compounded semiannually. Thereafter, $500 is deposited in the account at the end of every six months for five years. The value of the account at the end of five years is A) $ B) $ C) $ D) $ E) $ ) Suppose a person invests $20,000 in a business venture that guarantees the same cash flow at the end of every quarter for four years. If the investment earns interest at the rate of 16% compounded quarterly, then each cash flow is A) $ B) $ C) $ D) $ E) $ Page 209
11 18) Consider the following annuity: $2000 due at the end of each year for two years, and $3000 due thereafter at the end of each year for three years. At an interest rate of 4% compounded annually, the present value of the annuity is A) $12, B) $11, C) $10, D) $10, E) $9, ) Suppose a company establishes a sinking fund to replace equipment that has a salvage value of $50,000. The company deposits $20,000 into the fund at the end of every six months. If interest is earned at the rate of 8% compounded semiannually, the value of the fund at the end of six years is A) $137, B) $187, C) $237, D) $250, E) $300, SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 20) Find the sum of the geometric series: ) Find the sum of the geometric series: ) Find the present value of an annuity of $200 per month for years at an interest rate of 7% compounded monthly. 23) Find the amount of an annuity of payments of $150 at the end of every month for 3 years at the rate of 4% compounded monthly. Also find the compound interest. 24) A rubber ball always bounces back 2 3 of its previous height. If the ball is thrown up to a height of 30 feet, give the first five heights of the ball. 25) A company earns a profit of $2000 in its first month. Suppose its profit increases by 10% each month for two years. Find the amount of profit the company earns in its sixth and sixteenth months. 26) A company repays a $50,000 loan by paying 10% of the outstanding loan each month. Find the amount the company pays in the fourth and twentieth months. 27) $200 is invested at the rate of 6% compounded monthly for 5 months. List the compound amounts at the end of each month as a geometric sequence. 28) $200 is invested at the rate of 4.5% compounded semiannually for 8 years. Find the compound amounts at the end of the 2nd, 4th, and 8th years. 29) $200 is invested at the rate of 3.5% compounded quarterly for six and a half years. How many terms are in the geometric sequence formed by the amounts at the end of each quarter? 30) A ball rebounds 3 4 of its previous height after each bounce. If the ball is tossed up to a height of 16 feet, how far has it traveled in the air when it hits the ground for the fifteenth time? Page 210
12 31) A ball rebounds 2 of its previous height after each bounce. If the ball is dropped from a height of 27 feet, how 3 far has it traveled in the air when it hits the ground for the twentieth time? 32) A ball rebounds 3 5 of its previous height after each bounce. If the ball is dropped from a height of 20 meters, how far has it traveled in the air when it hits the ground for the sixth time? 33) A company earns a profit of $5000 in its first month. Suppose its profit decreases by 10% each month for one year. Find the amount of profit the company earns in its first year. 34) A company repays a $50,000 loan by paying 10% of the outstanding loan each month. How much has the company paid back after two years? 35) A company repays a $40,000 loan by paying 20% of the outstanding loan every four months for five years and then pays off the rest. How much was the companyʹs final payment? 36) What is the present value of an annuity of $300 per quarter for five years at an interest rate of 4.5% compounded quarterly? 37) What is the present value of an annuity of $1000 per month for ten years at an interest rate of 6.3% compounded monthly? 38) After putting $20,000 down on a piece of property, a man began paying $500 a month for ten years. Given an interest rate of 8% compounded monthly, how much would the property cost if the man had paid for it in cash? 39) After putting $10,000 down on a piece of property, a woman began paying $2500 a quarter for nine years. Given an interest rate of 7.75% compounded quarterly, how much would the property cost if the woman had paid for it in cash? 40) Given a payment of $800 per quarter for five years, use a graphing calculator to graph the present value A as a function of the interest rate per quarter r. Determine the nominal interest rate if the present value of the annuity is $14, ) Given an interest rate of 7.25% compounded monthly, find the present value of the following annuity: $700 at the end of each month for three years and $900 at the end of each month for five more years. 42) Given an interest rate of 4.6% compounded semiannually, find the present value of the following annuity: $2100 at the end of every six months for six years and $3000 at the end of every six months for four more years. 43) Suppose a woman purchases a building with an initial down payment of $40,000, and then makes monthly payments: $1500 at the end of each month for four years and $2000 at the end of each month for six more years. Given an interest rate of 5.5% compounded monthly, find the present value of the payments and the list price of the building. (Round your answer to the nearest dollar.) 44) If $30,000 is used to purchase an annuity consisting of equal payments at the end of each quarter for the next 5 years and the interest rate is 8% compounded quarterly, find the amount of each payment. Page 211
13 45) If $5000 is used to purchase an annuity consisting of equal payments at the end of each month for the next years and the interest rate is 6% compounded monthly, find the amount of each payment. 46) If $25,000 is used to purchase an annuity consisting of equal payments at the end of each year for the next 8 years and the interest rate is 5% compounded annually, find the amount of each payment. 47) If $12,000 is used to purchase an annuity consisting of equal payments at the end of every six months for the next 7 years and the interest rate is 6.2% compounded semiannually, find the amount of each payment. 48) Given an annuity with equal payments at the end of each month for six years and an interest rate of 5.3% compounded monthly, use a graphing calculator to graph the present value A as a function of the monthly payment R. Determine the monthly payment if the present value of the annuity is $30, ) The premiums on an insurance policy are $20 a month, payable at the beginning of each month. If the policy holder wishes to pay 1 yearʹs premiums in advance, how much should be paid provided that the interest rate is 5.1% compounded monthly? 50) The premiums on an insurance policy are $80 every six months, payable at the beginning of each six month period. If the policy holder wishes to pay 1 yearʹs premiums in advance, how much should be paid provided that the interest rate is 4.3% compounded semiannually? 51) A woman makes house payments of $4200 at the beginning of every quarter. If the woman wishes to pay yearʹs worth of payments in advance, how much should she pay provided that the interest rate is 5.4% compounded quarterly? 52) Find the amount of an annuity consisting of payments of $100 paid at the end of each quarter for five years at the rate of 5% compounded quarterly. Also find the compound interest. 53) Suppose you deposit $200 at the end of every month into a bank account that pays 6% compounded monthly. After six years, how much will you have? 54) Suppose Lena deposits $500 at the end of every month into a bank account that pays 5.4% compounded monthly. After five years, how much will she have? 55) Find the future value of an annuity due consisting of payments of $100 paid at the beginning of each quarter for five years at the rate of 5% compounded quarterly. 56) Suppose you deposit $200 at the beginning of every month into a bank account that pays 6% compounded monthly. After six years, how much will you have? 57) Suppose Lena deposits $500 at the beginning of every month into a bank account that pays 5.4% compounded monthly. After five years, how much will she have? Page 212
14 58) Suppose a truck costing $36,000 is to be replaced at the end of 10 years, at which time it will have a resale value of $12,000. In order to provide money at the time for a new truck costing $40,000, a sinking fund is set up into which equal payments are placed at the end of every six months. If the fund earns 6% compounded semiannually, what should each payment be? 59) Suppose a machine costing $12,000 is to be replaced at the end of 7 years, at which time it will have a salvage value of $6000. In order to provide money at that time for a new machine costing $15,000, a sinking fund is set up into which equal payments are placed at the end of every quarter. If the fund earns 5.6% compounded quarterly, what should each payment be? 60) In order to establish a sinking fund of $125,000, how much will have to be invested at the end of each year at the rate of 11.2% compounded annually for 8 years? 61) Suppose the Laus wish to save $36,000 for a down payment in three years. If they make payments at the end of every month into an account paying 7.5% compounded monthly, what size payments should they make? 62) Suppose a machine will yield a net of $200 per month for 5 years, after which the machine would be worthless. How much should the firm pay for the machine if it wants to earn 5% annually on its investment and also set up a sinking fund to replace the purchase price? For the fund, assume monthly payments and a rate of 4% annually. 63) Suppose you wish to purchase a mine that will yield an annual return of $32,000 for 12 years, after which the mine will have no value. You want to earn 8% annually on this investment and also set up a sinking fund to replace the purchase price. If money is placed in the fund at the end of each year and earns 6.2% compounded annually, how much should you pay for the mine? 64) Suppose a diagnostic machine will yield a net of $1000 per quarter for 5 years, after which the machine can be sold for $1000. How much should a firm pay for the machine if it wants to earn 7.5% annually on its investment and also set up a sinking fund to replace the purchase price? For the fund, assume quarterly payments and a rate of 5.5% compounded quarterly. 65) Suppose you wish to purchase a factory that will yield an annual return of $12,000 for 12 years, after which the factory will have no value. You want to earn 8.25% annually on your investment and also set up a sinking fund to replace the purchase price. If money is placed in the fund at the end of each year and earns 4.2% compounded annually, how much should you pay for the factory? 66) Find the Present Value of an ordinary annuity with semiannual payments of $450 for 30 years at 6% compounded semiannually. 67) Find the Present Value of an ordinary annuity with quarterly payments of $250 for 40 years at 7.25% compounded quarterly. 68) Find the Present Value of an ordinary annuity with monthly payments of $125 for 10 years at 4.5% compounded monthly. 69) Find the Present Value of an annuity due with semiannual payments of $350 for 35 years at 6.25% compounded semiannually. Page 213
15 70) Find the Present Value of an annuity due with quarterly payments of $2,750 for 27 years at 7.8% compounded quarterly. 71) Find the Present Value of an annuity due with monthly payments of $200 for 17 years at 5.25% compounded monthly. 72) Find the Future Value of an ordinary annuity with semiannual payments of $475 for 30 years at 6.15% compounded semiannually. 73) Find the Future Value of an ordinary annuity with quarterly payments of $300 for 30 years at 7.5% compounded quarterly. 74) Find the Future Value of an ordinary annuity with monthly payments of $250 for 40 years at 6.8% compounded monthly. 75) Find the Future Value of an annuity due with semiannual payments of $6,250 for 21 years at 4.25% compounded semiannually. 76) Find the Future Value of an annuity due with quarterly payments of $550 for 32 years at 3.75% compounded quarterly. 77) Find the Future Value of an annuity due with monthly payments of $250 for 26 years at 6% compounded monthly. 78) After graduating from college and gaining employment, you decide to open an IRA to help save for retirement. If the IRA earns 6.15% compounded monthly and you deposit $250 into this IRA at the end of each month, what will be the amount you have when you retire 43 years later? 79) You wish to be a millionaire when you retire. To accomplish this you decide to open up an IRA and make equal monthly payments at the end of each month. If the IRA earns 7.5% compounded monthly and you know you will retire in 40 years, what must be the monthly payment to obtain your $1,000,000? 5.5 Amortization of Loans SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A $5000 loan is to be repaid over three years by equal payments due at the end of every quarter. If interest is at the rate of 20% compounded quarterly, determine (a) the quarterly payment and (b) the total interest paid. 2) A 20year loan for $100,000 is to be amortized by equal semiannual payments. If interest is at the nominal rate of 10% compounded semiannually, find (a) the semiannual payment; (b) the interest in the first payment; (c) the principal repaid in the first payment. Page 214
16 3) A debt of $600 is to be repaid by two equal yearly payments with interest at the rate of 5% compounded annually. Complete the following amortization schedule for this debt. Principal outstanding at Interest Payment at end Principal repaid Period beginning of period for period of period at end of period 1 2 Totals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) An $800 loan is amortized by equal quarterly payments over two years. If interest is at the rate of 16% compounded quarterly, then the quarterly payment is A) $ B) $ C) $ D) $ E) $ ) A $10,000 loan is amortized by equal semiannual payments over 5 years. If the interest rate is 8% compounded semiannually, then the principal repaid in the first payment is A) $ B) $ C) $ D) $ E) $ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) A person purchases a home for $130,000, makes a down payment of $30,000. Find the monthly payment if the person takes a loan for 25 years with an interest rate of 8% compounded monthly. 7) A person purchases a home for $130,000, makes a down payment of $30,000. Find the monthly payment if the person takes a loan for 15 years with an interest rate of 8% compounded monthly. 8) A person purchased a television set for $850 and agreed to pay it off by monthly payments of $50. If the store charges an interest rate of 9% compounded monthly, how many months will it take to pay off the debt? 9) A person amortizes a loan of $180,000 for a new home by obtaining a 30 year mortgage at the rate of 8.7% compounded monthly. Find (a) the monthly payment, (b) the total interest charges, and (c) the principal remaining after 10 years. 10) The Krishnans amortize a loan of $150,000 for a new home by obtaining a 40year mortgage at the rate of 10.2% compounded monthly. Find (a) the monthly payment, (b) the total interest charges, and (c) the principal remaining after 15 years. 11) Mary amortizes a loan of $80,000 for a new home by obtaining a 15 year mortgage at the rate of 9.9% compounded monthly. Find (a) the monthly payment, (b) the total interest charges, and (c) the principal remaining after 8 years. 12) James amortizes a loan of $210,000 for a new home by obtaining a 40 year mortgage at the rate of 7.5% compounded monthly. Find (a) the monthly payment, (b) the total interest charges, and (c) the principal remaining after 15 years. 13) A man bought a stereo system for $3500 and agreed to pay off the loan by making monthly payments of $79. If the store charges an interest rate of 11% compounded monthly, how many months will it take to pay off the debt? Page 215
17 14) Cyndi bought a multimedia home computer system for $4500 and agreed to pay off the loan by making monthly payments of $109. If the store charges an interest rate of 9.7% compounded monthly, how many months will it take to pay off the debt? 15) A couple bought a motorboat for $11,000 and agreed to pay off the loan by making monthly payments of $559. If the dealer charges an interest rate of 8.9% compounded monthly, how many months will it take to pay off the debt? 16) A man purchased a new laser printer for his computer for $1100 and agreed to pay off the loan by making monthly payments of $59. If the store charges an interest rate of 12.2% compounded monthly, how many months will it take to pay off the debt? 17) At a car dealership, you are given two options for financing a new car worth $16,000. Option 1: You can take out a 5 year loan at 0% A.P.R. compounded monthly, or Option 2: You can get $3,000 cash back and finance the rest at 4.9% A.P.R. compounded monthly for 5 years. Which is the better option for you? Page 216
18 Ch. 5 Mathematics of Finance Answer Key 5.1 Compound Interest 1) % 2) 7 3) $ ) B 5) A 6) % 7) 6.09% 8) 6.99% 9) 4% 10) 6% 11) % 12) 37.49% 13) 5% 14) 4.63% 15) 4.65% 16) 3.5% 17) 5.51% 18) 3.47% 19) 3.67% 20) 4 years 21) 9 years 22) years 23) years 24) 10 years 25) %, 12.1% 26) %, 12.7% 27) %, % 28) %, % 29) % 30) 62,587 31) $24,198 32) $201,587 33) $14,683 34) years 35) years 36) years 37) years 38) 4.7% annually; $ ) 6.5% semiannually; $ ) 4.66% compounded 360 times a year 41) 5.53% daily. $ ) The first rate is better; the second investment earns more. 43) The compound amount is $1, ) The accumulated amount is $7, ) The compound amount is $7, ) a) The compound amount is $4, b) The compound interest is $1, Page 217
19 47) a) The compound amount is $18, b) The compound interest is $3, ) The accumulated amount is $13, ) The compound amount is $7, Present Value 1) $ ) $ ) 5000(1.05) = 3000(1.05) (1.05)2 + x 4) (a) $ (b) yes 5) B 6) $144, ) $ ) $ ) $ ) $ ) $ ) $ ) $ ) $12, ) $11, ) $ ) $ ) $ ) $ ) $ ) the friendʹs business 22) 6.78% 23) the business venture 24) the certificate of deposit 25) $658.68; no 26) $357.00; yes 27) $948.19; no 28) $632.36; yes 29) less than 7.918% 30) less than 4.742% 31) The present value is $4, ) The present value is $ ) The present value is $2, ) The present value is $1, ) The present value is $4, Interest Compounded Continuously 1) $1522 2) $ ) 8.33% 4) 10.52% 5) ) 8.7 7) $60,653 8) $406,570 9) C 10) D 11) A 12) A 13) % Page 218
20 14) % 15) % 16) $ ) The amount in the continuously compounded account is only slightly more that the account compounded semiannually, and although the difference is getting bigger, it is doing so very slowly. 18) The amount in the continuously compounded account is only slightly more that the account compounded monthly, and although the difference is getting bigger, it is doing so very slowly. 19) The graph looks roughly linear, which means that the effective rate increases about the same amount per incremental change in the annual rate regardless of what the initial annual rate is. 20) The graph shows that the earlier you invest the money, the less you need to invest. 21) The graph shows that the earlier you invest the money, the less you need to invest. 5.4 Annuities 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A 11) $12, ) $144, ) The amount of the investment is $294, after 21 yrs. 14) (a) $ (b) $ ) $ ) D 17) C 18) B 19) E 20) ) ) $13, ) $5,727.23; $ ) 30 ft, 20 ft, ft, ft, ft 25) $ , $ ) $3645, $ ) $201, $202, $203.02, $204.03, $ ) $218.62, $238.97, $ ) 26 30) ft 31) ft 32) m 33) $35, ) $46,012 35) $ ) $ ) $88, ) $61, ) $74, ) 5.23% 41) $58, Page 219
21 42) $38, ) $162,788; $202,788 44) $ ) $ ) $ ) $ ) $ ) $ ) $ ) $24, ) $ ; $ ) $17, ) $34, ) $ ) $17, ) $34, ) $ ) $ ) $10, ) $ ) $10,390 63) $230,900 64) $21,689 65) $80,921 66) $12, ) $13, ) $12, ) $ ) $125, ) $27, ) $79, ) $132, ) $620, ) $426, ) $136, ) $187, ) $633, ) $ Amortization of Loans 1) (a) $ (b) $ ) (a) $ (b) $ (c) $ ) Principal outstanding at Interest Payment at end Principal repaid Period beginning of period for period of period at end of period Totals ) C 5) D 6) $ ) $ ) months, approximately Page 220
22 9) (a) $ (b) $327, (c) $160, ) (a) $ (b) $472, (c) $140, ) (a) $ (b) $73,864 (c) $51, ) (a) $ (b) $453,336 (c) $149, ) 58 months 14) 51 months 15) 22 months 16) 21 months. 17) Take the $3,000 cash back and the 4.9% A.P.R. loan Page 221
Compound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
More informationFinite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan
Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationSection 8.1. I. Percent per hundred
1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)
More informationSolutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.
Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationIndex Numbers ja Consumer Price Index
1 Excel and Mathematics of Finance Index Numbers ja Consumer Price Index The consumer Price index measures differences in the price of goods and services and calculates a change for a fixed basket of goods
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM0905. January 14, 2014: Questions and solutions 58 60 were
More informationChapter 22: Borrowings Models
October 21, 2013 Last Time The Consumer Price Index Real Growth The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor
More informationUniversity of Rio Grande Fall 2010
University of Rio Grande Fall 2010 Financial Management (Fin 20403) Practice Questions for Midterm 1 Answers the questions. (Or Identify the letter of the choice that best completes the statement if there
More informationChapter 3 Mathematics of Finance
Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the
More informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
More informationExample. L.N. Stout () Problems on annuities 1 / 14
Example A credit card charges an annual rate of 14% compounded monthly. This month s bill is $6000. The minimum payment is $5. Suppose I keep paying $5 each month. How long will it take to pay off the
More information1. Annuity a sequence of payments, each made at equally spaced time intervals.
Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology
More informationFinance 197. Simple Onetime Interest
Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More information300 Chapter 5 Finance
300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationCheck off these skills when you feel that you have mastered them.
Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of
More informationE INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is
E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =
More informationPresent Value (PV) Tutorial
EYK 151 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
More informationThe Compound Amount : If P dollars are deposited for n compounding periods at a rate of interest i per period, the compound amount A is
The Compound Amount : If P dollars are deposited for n compounding periods at a rate of interest i per period, the compound amount A is A P 1 i n Example 1: Suppose $1000 is deposited for 6 years in an
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM0905. April 28, 2014: Question and solutions 61 were added. January 14, 2014:
More informationUndergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics
Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10,
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationChapter 3 Equivalence A Factor Approach
Chapter 3 Equivalence A Factor Approach 31 If you had $1,000 now and invested it at 6%, how much would it be worth 12 years from now? F = 1,000(F/P, 6%, 12) = $2,012.00 32 Mr. Ray deposited $200,000
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationCHAPTER 1. Compound Interest
CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the present value for the given future amount. Round to the nearest cent. 1) A = $4900,
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More informationVilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis
Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................
More informationMath 1332 Test 5 Review
Name Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month. 1) $1660 at 6% for 4 months Find the future value of the deposit if the
More informationQuestion 31 38, worth 5 pts each for a complete solution, (TOTAL 40 pts) (Formulas, work
Exam Wk 6 Name Questions 1 30 are worth 2 pts each for a complete solution. (TOTAL 60 pts) (Formulas, work, or detailed explanation required.) Question 31 38, worth 5 pts each for a complete solution,
More informationExercise 1 for Time Value of Money
Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing
More informationLoans Practice. Math 107 Worksheet #23
Math 107 Worksheet #23 Loans Practice M P r ( 1 + r) n ( 1 + r) n =, M = the monthly payment; P = the original loan amount; r = the monthly interest rate; n = number of payments 1 For each of the following,
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationFinance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date
1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand
More informationFuture Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)
MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the
More informationSimple Interest. and Simple Discount
CHAPTER 1 Simple Interest and Simple Discount Learning Objectives Money is invested or borrowed in thousands of transactions every day. When an investment is cashed in or when borrowed money is repaid,
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationChapter 21: Savings Models
October 16, 2013 Last time Arithmetic Growth Simple Interest Geometric Growth Compound Interest A limit to Compounding Problems Question: I put $1,000 dollars in a savings account with 2% nominal interest
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationBank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.
ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationICASL  Business School Programme
ICASL  Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business
More informationThe following is an article from a Marlboro, Massachusetts newspaper.
319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston  Last week
More informationFind the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually
Exam Name Find the compound amount for the deposit. Round to the nearest cent. 1) $1200 at 4% compounded quarterly for 5 years Find the effective rate corresponding to the given nominal rate. Round results
More informationWarmup: Compound vs. Annuity!
Warmup: Compound vs. Annuity! 1) How much will you have after 5 years if you deposit $500 twice a year into an account yielding 3% compounded semiannually? 2) How much money is in the bank after 3 years
More informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationSample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
More informationFinance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.
Chapter 1 Finance 331 What is finance?  Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: 
More informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
More informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More informationChapter 5 Present Worth
Chapter 5 Present Worth 51 Emma and her husband decide they will buy $1,000 worth of utility stocks beginning one year from now. Since they expect their salaries to increase, they will increase their
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationThe Institute of Chartered Accountants of India
CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
More informationChapter 03  Basic Annuities
31 Chapter 03  Basic Annuities Section 7.0  Sum of a Geometric Sequence The form for the sum of a geometric sequence is: Sum(n) a + ar + ar 2 + ar 3 + + ar n 1 Here a = (the first term) n = (the number
More informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
More informationIf P = principal, r = annual interest rate, and t = time (in years), then the simple interest I is given by I = P rt.
13 Consumer Mathematics 13.1 The Time Value of Money Start with some Definitions: Definition 1. The amount of a loan or a deposit is called the principal. Definition 2. The amount a loan or a deposit increases
More informationThe values in the TVM Solver are quantities involved in compound interest and annuities.
Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
More information2. How many months will it take to pay off a $9,000 loan with monthly payments of $225? The APR is 18%.
Lesson 1: The Time Value of Money Study Questions 1. Your mother, who gave you life (and therefore everything), has encouraged you to borrow $65,000 in student loans. The interest rate is a recordlow
More informationChapter 4: Time Value of Money
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
More informationModule 5: Interest concepts of future and present value
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationTime Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...
Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value
More informationChapter 2 Finance Matters
Chapter 2 Finance Matters Chapter 2 Finance Matters 2.1 Pe r c e n t s 2.2 Simple and Compound Interest 2.3 Credit Cards 2.4 Annuities and Loans Chapter Summary Chapter Review Chapter Test Handling personal
More informationTopics. Chapter 5. Future Value. Future Value  Compounding. Time Value of Money. 0 r = 5% 1
Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationQuestion Details JModd7 5.1.003. [1633641] Question Details JModd7 5.1.005.CMI. [1617591] Question Details JModd7 5.2.011.CMI.
1 of 7 MATH 179: Final Exam Review (3420833) Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Instructions Here are 26 questions from all the sections we've covered... I am
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More informationInternational Financial Strategies Time Value of Money
International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value
More informationChapter 3 Understanding Money Management. Nominal and Effective Interest Rates Equivalence Calculations Changing Interest Rates Debt Management
Chapter 3 Understanding Money Management Nominal and Effective Interest Rates Equivalence Calculations Changing Interest Rates Debt Management 1 Understanding Money Management Financial institutions often
More informationApplications of Geometric Se to Financ Content Course 4.3 & 4.4
pplications of Geometric Se to Financ Content Course 4.3 & 4.4 Name: School: pplications of Geometric Series to Finance Question 1 ER before DIRT Using one of the brochures for NTM State Savings products,
More information4 Annuities and Loans
4 Annuities and Loans 4.1 Introduction In previous section, we discussed different methods for crediting interest, and we claimed that compound interest is the correct way to credit interest. This section
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationExam 2 Study Guide. o o
1. LS7a An account was established 7 years ago with an initial deposit. Today the account is credited with annual interest of $860. The interest rate is 7.7% compounded annually. No other deposits or withdrawals
More information21.1 Arithmetic Growth and Simple Interest
21.1 Arithmetic Growth and Simple Interest When you open a savings account, your primary concerns are the safety and growth of your savings. Suppose you deposit $1000 in an account that pays interest at
More informationFinance. Simple Interest Formula: I = P rt where I is the interest, P is the principal, r is the rate, and t is the time in years.
MAT 142 College Mathematics Finance Module #FM Terri L. Miller & Elizabeth E. K. Jones revised December 16, 2010 1. Simple Interest Interest is the money earned profit) on a savings account or investment.
More informationMatt 109 Business Mathematics Notes. Spring 2013
1 To be used with: Title: Business Math (Without MyMathLab) Edition: 8 th Author: Cleaves and Hobbs Publisher: Pearson/Prentice Hall Copyright: 2009 ISBN #: 9780135136874 Matt 109 Business Mathematics
More informationChapter 3 Present Value
Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value
More informationActivity 3.1 Annuities & Installment Payments
Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.
More informationChapter 2. CASH FLOW Objectives: To calculate the values of cash flows using the standard methods.. To evaluate alternatives and make reasonable
Chapter 2 CASH FLOW Objectives: To calculate the values of cash flows using the standard methods To evaluate alternatives and make reasonable suggestions To simulate mathematical and real content situations
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation
More information