Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually

Transcription

1 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 to the nearest 0.01 percentage points. 2) 15% compounded semiannually Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated. 3) $16,500 at 10% compounded annually for 9 yr 4) $8000 at 8% compounded semiannually for 2 yr Solve the problem. 5) June made an initial deposit of $4300 in an account for her son. Assuming an interest rate of 8% compounded quarterly, how much will the account be worth in 19 years? 6) A municipal bond with a face value of $5000 in ten years can be purchased now for $2345. Find the simple interest rate. Round to the nearest tenth of a percent. 7) Andrea Gilford's savings account has a balance of $4473. After 5 years, what will the amount of interest be at 6% compounded quarterly? 8) Barbara knows that she will need to buy a new car in 6 years. The car will cost $15,000 by then. How much should she invest now at 12%, compounded quarterly, so that she will have enough to buy a new car? 9) Southwest Dry Cleaners believes that it will need new equipment in 10 years. The equipment will cost $26,000. What lump sum should be invested today at 6% compounded semiannually, to yield $26,000? Find the future value of the annuity due. 10) Payments of $500 made at the beginning of each year for 7 years at 12% compounded annually 11) $200 deposited at the beginning of each quarter for 11 years at 6% compounded quarterly Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated. 12) R = $1,000, i = 0.06, n = 11 13) R = $2,500, i = 9% interest compounded quarterly for 16 years Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given is per period. 14) $68,000; money earns 7.2% compounded monthly for years 1

2 15) $7000; money earns 2% compounded annually; 11 annual payments 16) $91,000; money earns 5% compounded quarterly for years Find the periodic payment that will render the sum. 17) S = $45,000, interest is 18% compounded monthly, payments made at the end of each month for 3 years 18) S = $220,000, interest is 10% compounded semiannually, payments made at the end of each semiannual period for 8 years 19) S = $58,000, interest is 12% compounded quarterly, payments are made at the end of each quarter for 5 years Solve the problem. 20) Which of the following investments is larger after 10 years? A) An initial amount of $10,000 is deposited with $500 deposited monthly, with interest earned at 5% compounded monthly. B) An initial amount of $12,000 is deposited with $6000 deposited annually, with interest earned at 5% compounded annually. 21) If $900,000 is to be saved over 20 years, how much should be deposited annually if the investment earns 8.75% interest compounded annually? A) $22, B) $14, C) $18, D) $27, Solve the problem. Round to the nearest cent. 22) At the end of every 3 months, Teresa deposits $100 into an account that pays 4% compounded quarterly. After 3 years, she puts the accumulated amount into a certificate of deposit paying 7.5% compounded semiannually for 1 year. When this certificate matures, how much will Teresa have accumulated? 23) $ is deposited at the end of each month for 2 years in an account paying 12% interest compounded monthly. Find the amount of the account. 24) If Bob deposits $5,000 at the end of each year for 8 years in an account paying 10% interest compounded annually, find the amount he will have on deposit. 25) How much should be deposited semiannually into a sinking fund over 5 years to accumulate $170,000 if the money earns 8% compounded semiannually? 26) Green Thumb Landscaping wants to build a $125,000 greenhouse in 2 years. The company sets up a sinking fund with payments made quarterly. Find the payment into this fund if the money earns 12% compounded quarterly. 27) Mark wants to start an IRA that will have $250,000 in it when he retires in 27 years. How much should he invest quarterly in his IRA to do this if the interest is 16% compounded quarterly? 2

3 Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for 20 years at the given interest rate, compounded annually. 28) $100,000 at 5% 29) $250 at 3% Find the monthly house payment necessary to amortize the following loan. 30) In order to purchase a home, a family borrows $75,000 at 13% for 15 yr. What is their monthly payment? 31) In order to purchase a home, a family borrows $428,000 at 12.1% for 30 yr. What is their monthly payment? Round the answer to the nearest cent. Find the payment necessary to amortize the loan. 32) $9000; 9% compounded semiannually; 10 semiannual payments 33) $60,000; 8% compounded annually; 10 annual payments Find the present value of the ordinary annuity. 34) Payments of $90,000 made semiannually for 12 years at 12% compounded semiannually 35) Payments of $3000 made annually for 25 years at 9% compounded annually Solve the problem. 36) Tasha borrowed $12,000 to purchase a new car at an annual interest rate of 10%. She is to pay it back in equal monthly payments over a 3 year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar. 37) Julio buys a bike which has a cash price of $250. He agrees to take a one-year loan for the entire amount at 27%, payable in 12 installments. After 8 of the 12 payments, he gets some birthday money and decides to pay off his loan. Find the unpaid balance. Use an amortization table to solve the problem. Round to the nearest cent. 38) The monthly payments on a $51,000 loan at 12% annual interest are $ How much of the first monthly payment will go toward the principal? 39) The monthly payments on a $63,000 loan at 14% annual interest are $ How much of the first monthly payment will go toward interest? 3

4 Use the data to make a histogram. 40) Alice asked 20 people how many magazines they purchased in the last year. Use four intervals starting with Find the mean. Round to the nearest tenth. 41) Value Frequency Find the mean for the list of numbers. 42) 18, 4, 24, 18 (Round to the nearest tenth) Find the median. 43) 9, 2, 29, 19, 45, 31, 31 Find the mode or modes. 44) 79, 58, 32, 58, 29, 79 45) 61, 25, 61, 13, 25, 29, 56, 61 Find the standard deviation. 46) 10, 10, 17, 20, 6, 8, 9, 20, 18 47) 17, 19, 11, 14, 9, 16, 8, 14, 18, 25 Find the standard deviation for the given data. 48) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below. Round results to four decimal places Find the percent of the total area under the standard normal curve between the given z-scores. 49) z = 0.0 and z =

5 50) z = and z = ) z = 0.07 and z = 2.45 Find the percent of the total area under a normal curve that is contained within the specified interval. 52) Between z = 1.41 and z = ) Between z = and z = ) Between the mean and.35 standard deviations from the mean A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last the specified period of time. 55) Between 540 hours and 780 hours 56) Less than 200 hours 57) Between 290 hours and 540 hours Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. 58) At a local market, the average weekly grocery bill is $57.85 with a standard deviation of $ What is the lowest amount spent by the upper 25% of market customers? 59) A certain grade egg must weigh at least 2.5 oz. If the average weight of an egg is 1.5 oz, with a standard deviation of.4 oz, how many eggs in a sample of 9 dozen would you expect to be over the 2.5 oz size? At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are: 60) Greater than 13.4 seconds 61) Between 14.3 and 16.1 seconds 62) Between 16.1 and 17 seconds A die is rolled five times and the number of twos that come up is tallied. Find the probability of getting the indicated result. 63) Two comes up four times. Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of the indicated results. 64) Less than 235 heads 65) 265 heads or more 5

6 Find the probability of the result using the normal curve approximation to the binomial distribution. 66) A 56-question multiple choice test has 4 possible answers for each question and a student chooses the answers to each problem at random. A student selects 16 correct answers. 67) A battery company has found that the defective rate of its batteries is Each day, 400 batteries are randomly tested. On Tuesday, 14 are found to be defective. 68) The probability that a radish seed will germinate is 0.7. The gardener plants 140 seeds and she harvests 100 radishes. Solve the problem using the normal curve approximation to the binomial distribution. 69) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions. 70) Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective. 71) The probability that a radish seed will germinate is.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate. 6

7 Answer Key Testname: 1324-STAT-FIN-PT 1) $ ) 15.56% 3) $ ) $ ) $19, ) 7.9% 7) $ ) $ ) $14, ) $ ) $12, ) $14, ) $350, ) $ ) $ ) $ ) $ ) $ ) $ ) B 21) C 22) $ ) $20, ) $57, ) $14, ) $14, ) $ ) $1,246, ) $ ) $ ) $ ) $ ) $ ) $1,129, ) $29, ) $ ) $ ) $ ) $

8 Answer Key Testname: 1324-STAT-FIN-PT 40) 41) ) 16 43) 29 44) 79, 58 45) 61 46) ) ) ) ) ) ) 7.7% 53) 43.5% 54) 13.68% 55) ) 7 57) ) $ ) 1 egg 60) 97.7% 61) 68% 62) 13.6% 63) ) ) ) ) ) ) ) )