# Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.

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1 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 Future Value of \$1 3 8% Future Value of \$1 6 4% Future Value of \$1 12 2% Present Value of \$1 3 8% Present Value of \$1 12 8% Present Value of \$1 12 2% Present Value of Annuity of \$1 in Arrears 3 8% Present Value of Annuity of \$1 in Arrears 3 2% Present Value of Annuity of \$1 in Arrears 12 2% Future Value of Annuity of \$1 in Arrears 3 8% Future Value of Annuity of \$1 in Arrears 3 2% Future Value of Annuity of \$1 in Arrears 12 2% Which of the following amounts is nearest the sum of money that must be invested today at 8% per year, compounded quarterly, in order to have \$5,000 in 3 years? (a) \$3,942 (b) \$6,299 (c) \$3,969 (d) \$1, A non interest-bearing note that pays \$5,000 three years from today is issued in exchange for used equipment. Which of the following amounts would be recorded as the acquisition value of the equipment, the amount the note is worth today if the discount rate appropriate for such notes is 8% per annum? (a) \$3,942 (b) \$6,299 (c) \$3,969 (d) \$1,940

2 3. From the above question, the entry to record the issue of a note for the used equipment on our books would include a: (a) Dr Used Equipment \$5,000 (b) Cr Note Payable \$3,969 (c) Dr Discount on Note Payable \$1,031 (d) Cr Discount on Note Payable \$1, A company is obligated to make annual payments to a pension fund at the end of the next three years. The present value of those payments is to be \$100,000. Which of the following amounts is nearest the amount which must be paid annually if the fund is projected to earn interest at the rate of 8% per year? (a) \$33,333 (b) \$26,461 (c) \$41,990 (d) \$38, Which one of the following statements is true? (a) Present values are always less then future values (b) Present values are always greater then future values (c) Present values are always equal to future values (d) None of the above 6. Compounded interest is (a) interest only paid on the principal (b) interest only paid on interest (c) interest paid on principal and interest (d) none of the above 7. The Rule of 72 is used (a) to find out how much interest has been paid when interest is compounded (b) to find out how much interest is owed when interest is compounded (c) to find out how many years interest doubles in 72 years when interest is compounded (d) to find out how many years it takes money to double when interest is compounded

3 8. If 8% is compounded quarterly for 3 years then the interest rate (r) for a single period used in a time-value money calculation would be (a) 8% (b) 4% (c) 3% (d) 2% 9. If 8% is compounded quarterly for 3 years then the number of periods used in a time-value money calculation would be (a) 3 periods (b) 4 periods (c) 8 periods (d) 12 periods 10. A series of identical cash flows (inflow or outflow) is referred to as a(n) (a) single sum (b) annuity (c) sum series (d) identical series 11. An ordinary annuity is when (a) the cash flow occurs at the end of a period (b) the cash flow occurs at the beginning of a period (c) the cash flow occurs at the middle of a period (d) the cash flow occurs at the terms agreed upon 12. Which one of the following statements is true? (a) Interest makes a dollar today worth less than a dollar tomorrow (b) Interest makes a dollar today worth more than a dollar tomorrow (c) Interest makes a dollar today worth the same as a dollar tomorrow (d) Interest has no affect on the value of a dollar

4 13. If you borrowed \$1,500 for a 5 year period, with a simple interest rate of 10% per annum, the total interest to be paid would be (a) \$1,500 (b) \$1,250 (c) \$1,000 (d) \$750 PROBLEM 2 What number of periods and rate per compounding period would you look up in the tables if given; (a) 12% per annum, for 5 years, compounded annually? (b) 12% per annum, for 5 years, compounded semiannually? (c) 12% per annum, for 5 years, compounded quarterly? (d) 12% per annum, for 5 years, compounded monthly? PROBLEM 3 Calculate the Future Value (FV) of; (a) \$100,000 invested for 5 years, compounded annually? (b) \$500,000 invested for 7.5 years at 4%, compounded semiannually? (c) \$200,000 invested for 8 years at 3% per annum? PROBLEM 4 Calculate the Present Value (PV) of; (a) \$100,000 due in 25 years at 4% compounded annually? (b) \$250,000 due in 6 years at 8% compounded quarterly? (c) \$200,000 due in 8 years at 3% per annum? PROBLEM 5 Assume at the beginning of 2002 Construction Co. deposits \$250 million in an account with BIG MONEY BANK as a commitment to a large construction project to be completed December 31, How much will be on deposit at the end of 4 years if interest is compounded semiannually at 10%?

5 PROBLEM 6 Your grandparents propose to give you \$4,000 for a road trip to the West Coast upon your successful completion of your degree at York University 3 years from now. They will fund the trip by investing a sum of money now at 6%. How much do your grandparents need to invest today in order to give you \$4,000 to fund your road trip 3 years from now? PROBLEM 7 York University would like to collect \$70,000 for the construction of a new parking lot in 4 years. If the University is able to deposit \$47,811 at the beginning of this year, what rate of interest, compounded annually, must the University receive to fund the project in 4 years? PROBLEM 8 You need \$150,000 four years from now to be able to pay off your mortgage. If you are earning 10% interest on your money at the bank. How much do you need to invest at the end of each year, so that at the end of the forth year you are able to pay of your mortgage? PROBLEM 9 How much money do you need to invest today, receiving an interest rate of 10% on your money, if you wish to withdraw \$32,321 at the end of each year for the next 4 years? PROBLEM 10 You have to repay Atkins Bank \$60,000 which you have borrowed today, plus 12% in four equal payments at the end of the next four years. How much is each payment? PROBLEM 11 Assume you decide to make five \$5,000 deposits into your saving account at the end of each of the next five years, so to accumulate enough money to pay off your student loan. What is the future value that will be on deposit at the end of the five years earning an annual interest of 3%? PROBLEM 12 You are an accounting student at Atkinson, completing a 5 year Accounting Program who lives on campus and rents an apartment. You pay \$6,000 at the end of each year for the next five years for rent. (a) What is the present value of the rental payments when the payments are discounted at a rate of 12% per year? (b) What is the present value if instead the rental payments were \$1,500 per quarter and payments are discounted at a rate of 12% compounded quarterly?

6 PROBLEM 13 You have just won the Super 7 Jackpot totaling \$20,000,000. You will be paid \$1,000,000 at the end of each of the next 20 years. What would that amount be in today s dollars if interest rates are currently 10%? PROBLEM 14 Calculate the future value of an annuity in arrears of; (a) 13 rents of \$100 at a rate of 1.5% per period? (b) 8 rents of \$850 at 6% per period? (c) 20 rents of \$400 at 4% per period? PROBLEM 15 Mr. Wong has \$500 to invest. He wants to know how much it will grow to if he invests it at 6% per year for 21 years? PROBLEM 16 Ms. Gorbachev wishes to have \$15,000 in her hands at the end of 8 years. How much must she invest now if money is worth 6% per year? PROBLEM 17 Mr. Pavorotti plans to set aside \$4,000 a year for the next 10 years. (a) How much will he have at the end of 10 years if he sets aside \$4,000 at the end of each year for the next 10 years and money is worth 8% per annum? (b) How much will he have at the end of 10 years if he sets aside \$2,000 at the end of each sixmonth period if money is worth 8% compounded semiannually? PROBLEM 18 Ms. Dodd turned 57 a week ago and wants to have \$450,000 saved by her 65 th birthday. How much must she deposit on each birthday (her 58 th to her 65 th inclusive) to have this amount if money is worth 9%?

7 PROBLEM 19 A friend would like to return to school full time beginning in four years. Your friend will need \$8,000 per year for each of the four years beginning in four years. How much should your friend invest for each of the next four years at 8%? PROBLEM 20 Expanding Corporation financed a \$700,000 expansion by mortgaging their head office building for seven years. They negotiated a rate of 10% per annum. a) What will the annual payments be, assuming payments are made annually at the end of the year? b) Complete the following amortization table for the mortgage: Year Payment Interest Reduction of Prinicpal Year 1? Year 2 Year 3 Year 4 Year 5 Year 6 Principal Balance outstanding \$700,000 c) How much is the interest expense in Year 3? d) What should be reported as the Mortgage liability on the balance sheet for Year 4?

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