Unit 4: Time Value of Money Concept - Practice Quiz

1 What does compounding calculate?

2 What does discounting calculate?

3 What is the one-period discount factor at an interest rate of ?

4 If earns interest for one year, what is its compounded value?

5 For a positive interest rate, what usually happens to future value when compounding becomes more frequent?

6 Which formula gives the future value of a single amount invested for periods at rate ?

7 Which formula gives the present value of a single future amount?

8 What is the present value of received in one year if the discount rate is ?

9 What is the future value of invested for one year at ?

10 If the discount rate increases while the future cash flow remains fixed, what happens to its present value?

11 What is an annuity?

12 When are payments made in an ordinary annuity?

13 When are payments made in an annuity due?

14 An ordinary annuity pays at the end of each year for two years. At , what is its future value at the end of year two?

15 With identical payments, periods, and a positive discount rate, how does the present value of an annuity due compare with that of an ordinary annuity?

16 What does the effective annual rate measure?

17 Which formula calculates the effective annual rate when the nominal annual rate is and compounding occurs times per year?

18 A nominal annual rate is compounded monthly. How does its effective annual rate compare with ?

19 What is the effective annual rate for a nominal rate of compounded semiannually?

20 If interest is compounded once per year, how does the effective annual rate compare with the nominal annual rate?

21 A company invests $12,500 for 3 years at an annual compound interest rate of 8%. What is the investment's future value?

22 A business expects to receive $30,000 four years from now. If its required return is 9% annually, what is the present value of this amount?

23 A firm deposits $20,000 at a nominal annual interest rate of 10%, compounded semiannually. How much will it have after 3 years?

24 At a discount rate of 8%, which alternative has the greater present value: receiving $9,000 today or $11,000 in two years?

25 A payment of $40,000 is due in 5 years. What amount invested today at 9% annual compound interest would be sufficient to meet the payment?

26 Two banks offer 8% annual interest. Bank A compounds annually, while Bank B compounds quarterly. On a $10,000 deposit held for 2 years, approximately how much more will Bank B provide?

27 A corporation deposits $5,000 at the end of each year for 4 years into an account earning 7% annually. What is the value immediately after the fourth deposit?

28 A company deposits $5,000 at the beginning of each year for 4 years into an account earning 7%. What is the account value at the end of year 4?

29 A machine is expected to generate $12,000 at the end of each year for 5 years. At an 8% discount rate, what is the present value of these cash flows?

30 A company borrows $100,000 at 10% annual interest and will repay it with four equal year-end payments. What is the annual payment?

31 An investment pays $6,000 at the end of every year indefinitely. If the required return is 7.5%, what is the investment's present value?

32 An investment will pay $10,000 at the end of years 3, 4, 5, and 6. If the discount rate is 6%, what is its present value today?

33 A bank quotes a nominal annual rate of 12%, compounded monthly. What is the effective annual interest rate?

34 Bank A offers 10% nominal interest compounded quarterly. Bank B offers 10.2% nominal interest compounded semiannually. Which bank offers the higher effective annual rate?

35 A savings account has an effective annual rate of 8.16% and compounds semiannually. What nominal annual rate does it quote?

36 An account has an effective annual rate of approximately 12.68% with monthly compounding. What is its nominal annual interest rate?

37 An investment earns a nominal annual rate of 7% with continuous compounding. What is its effective annual rate?

38 A project will generate $5,000 in year 1, $7,000 in year 2, and $9,000 in year 3. At an 8% discount rate, what is the project's present value?

39 A firm needs $75,000 in 4 years. If funds earn 6% compounded annually, how much must the firm invest today?

40 At a 6% discount rate, which payment option has the higher present value: $25,000 today or $9,000 at the end of each year for 3 years?

41 An investment earns effective annual returns of , , and over three successive years. What constant effective annual rate would produce the same ending value?

42 USD 50,000 earns a nominal rate of compounded monthly for 18 months, followed by a nominal rate of compounded quarterly for 2.5 years. What is the ending balance?

43 The effective annual spot rate is for each of the first two years. The effective annual forward rate for each of the following three years is . What is the present value of USD 250,000 due at the end of year 5?

44 An account receives USD 30,000 today and USD 20,000 at the end of year 2. Exactly USD 80,968.81 is withdrawn at the end of year 5, exhausting the account. What constant effective annual return did the account earn?

45 A risk-free claim pays USD 100,000 in three years. If the effective annual interest rate is for all maturities, what is its present value?

46 A project pays USD 40,000, USD 60,000, and USD 90,000 at the ends of years 1, 2, and 3. The corresponding effective annual spot rates are , , and . What is the project's present value?

47 An investor wants USD 200,000 of current purchasing power to grow at a real annual rate of for six years. Inflation is expected to be annually. Using the exact Fisher relation, what nominal amount is required at year 6?

48 A payment of USD 150,000 is due in 7.5 years. If the continuously compounded annual discount rate is , what is its present value?

49 How long will an investment take to double at a nominal annual rate of compounded monthly?

50 Two payments of USD 100,000 are due at the ends of years 4 and 8. At an effective annual rate of , what single payment at the end of year 6 is equivalent to both?

51 An ordinary annuity pays USD 25,000 annually from the end of year 6 through the end of year 15. At an effective annual discount rate of , what is its value today?

52 Eight equal deposits are made at the beginnings of years 1 through 8, starting today. If the account earns annually, what deposit produces USD 100,000 at the end of year 8?

53 A 12-payment growing annuity pays USD 30,000 at the end of year 1, with subsequent payments growing by annually. If the effective annual discount rate is , what is its present value?

54 A USD 500,000 loan is amortized by 20 equal end-of-year payments at effective annually. What balloon balance remains immediately after the seventh payment?

55 A perpetuity pays USD 10,000 at the end of the first quarter, and each quarterly payment grows by . The effective annual discount rate is , equivalent to per quarter. What is the perpetuity's present value?

56 A nominal annual rate of compounded quarterly must be replaced by an equivalent nominal annual rate compounded monthly. What monthly-compounded nominal rate is equivalent?

57 Which deposit quotation provides the greatest effective annual yield?

58 A 180-day Treasury bill with face value USD 100 is purchased for USD 96. Assume a 360-day year and that identical 180-day returns can be reinvested. What is the effective annual yield?

59 An investment accumulates by exactly over 15 months. What constant effective annual rate is equivalent?

60 A borrower signs a six-month loan with a face amount of USD 100,000 but receives only USD 98,000 after an upfront fee. The borrower must repay USD 104,000 after six months. Assuming the same six-month cost compounds, what is the effective annual borrowing rate?