Chapter 9 – Time Value of Money
1. An amount of money to be received in the future is worth less today than the stated amount. TRUE 2. Discounting refers to the growth process that turns $1 today into a greater value several periods in the future. FALSE 3. Compounding refers to the growth process that turns $1 today into a greater value several periods in the future. TRUE 4. The interest factor for the future value of a single sum is equal to (1 + n) i. FALSE 5. The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year. TRUE 6. The future value is the same concept as the way money grows in a bank account. TRUE 7. The present value of a positive future inflow can become negative as discount discount rates become higher and higher. FALSE 8. The formula PV = FV(1 + n) i will determine the present value of $1. FALSE 9. The interest factor for the present value of a single amount is the inverse of the future value interest factor. TRUE 10. Higher interest rates (discount rates) reduce the present value of amounts to be received in the future. TRUE 11. In determining the future value of an annuity, the final payment is not compounded at all. TRUE 12. The future value of an annuity assumes that the payments are received at the end of of the year and that the last payment does not compound. TRUE
13. The amount of annual a nnual payments necessary to accumulate a desired total can be found by reference to the present value of an annuity table. FALSE 14. If an individual' i ndividual'ss cost of capital were 10%, he/she would prefer to receive $107 at the end of one year rather than $100 right now. FALSE 15. Using semi-annual compounding rather than annual compounding will increase the future value of an annuity. TRUE 16. In paying off a mortgage loan, the amount of the periodic payment that goes goes toward the reduction of principal increases over over the life of the mortgage. TRUE 17. The time value of money concept becomes less critical as the prime rate increases. FALSE 18. Discounted at 6%, $1000 received three years from now is worth less than $800 received today. FALSE 19. Discounted at 6%, $1000 received at the end of each year for three years is worth less than $2,700 received today. TRUE 20. Under what conditions must a distinction be made between money to be received received today and money to be received in the future? A. A period of recession. B. When idle money can earn a positive return. C. When there is no risk of nonpayment in the future. D. When current interest rates are different from expected future rates. 21. As the compounding rate becomes lower and lower, the future value of inflows approaches A. 0 B. the present value of the inflows C. infinity D. need more information 22. If you invest $8,000 at 12% interest, how much will you have in 7 years? A. $18,016 B. $17,688 C. $3616 D. $80,712 23. In determining the future value of a single amount, one measures
A. the future value of periodic payments at a given interest rate. B. the present value of an amount discounted at a given interest rate. C. the future value of an amount allowed to grow at a given interest rate. D. the present value of periodic payments at a given interest rate. 24. The concept of time value of money is important to financial decision making because A. it emphasizes earning a return on invested capital. B. it recognizes that earning a return makes $1 worth more today than $1 received in the future. C. it can be applied to future cash flows in order to compare different streams of income. D. all of these 25. As the discount rate becomes higher and higher, the present value of inflows approaches A. 0 B. minus infinity C. plus infinity D. need more information 26. How much must you invest at 10% interest in order to see your investment grow to $5,000 in 5 years? A. $3,070 B. $3,415 C. $3,105 D. none of these 27. An annuity may be defined as A. a payment at a fixed interest rate. B. a series of payments of unequal amount. C. a series of yearly payments. D. a series of consecutive payments of equal amounts. 28. You are to receive $12,000 at the end of 5 years. The available yield on investments is 6%. What is the present value? A. $8,950 B. $9,000 C. $8,967 D. $8,230 29. As the interest rate increases, the present value of an amount to be received at the end of a fixed period A. increases. B. decreases. C. remains the same. D. Not enough information to tell. 30. As the time period until receipt increases, the present value of an amount at a fixed interest rate A. decreases.
B. remains the same. C. increases. D. Not enough information to tell. 31. To save for her newborn son's college education, Lea Wilson will invest $1,000 at the beginning of each year for the next 18 years. The interest rate is 12 percent. What is the future value? A. $7,690. B. $34,931. C. $63,440. D. $55,750. 32. The IF for the future value of an annuity is 4.641 at 10% for 4 years. If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be? A. $2,500 B. $2,000 C. $1,724 D. none of these55. 33. Mr. Blochirt is creating a college investment fund for his daughter. He will put in $850 per year for the next 15 years and expects to earn an 8% annual rate of return. How much money will his daughter have when she starts college? A. $11,250 B. $12,263 C. $24,003 D. $23,079 34. Mr. Nailor invests $5,000 in a money market account at his local bank. He receives annual interest of 8% for 7 years. How much return will his investment earn during this time period? A. $2,915 B. $3,570 C. $6,254 D. $8,570 35. Lou Lewis borrows $10,000 to be repaid over 10 years at 9 percent. Repayment of principal in the first year is: A. $1,558 B. $658 C. $742 D. $885 36. Sharon Smith will receive $1 million in 50 years. The discount rate is 14%. As an alternative, she can receive $2,000 today. Which should she choose? A. the $1 million dollars in 50 years. B. $2,000 today. C. she should be indifferent. D. need more information.
37. Pedro Gonzalez will invest $5,000 at the beginning of each year for the next 9 years. The interest rate is 8 percent. What is the future value? A. $58,471. B. $62,440. C. $67,435. D. $72,435. 38. Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate. A. $19,033 B. $27,870 C. $32,389 D. none of these 39. Dr. J. wants to buy a Dell computer which will cost $2,788 four years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn 7% annual return. How much should he set aside? A. $697.00 B. $627.93 C. $823.15 D. $531.81 40. Mr. Fish wants to build a house in 10 years. He estimates that the total cost will be $170,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed? A. Between 11% and 12% B. Between 8% and 9% C. 17% D. None of these 41. The shorter the length of time between a present value and its corresponding future value, A. the lower the present value, relative to the future value. B. the higher the present value, relative to the future value. C. the higher the interest rate used in the presentvaluation. D. none of these. 42. A dollar today is worth more than a dollar to be received in the future because A. risk of nonpayment in the future. B. the dollar can be invested today and earn interest. C. inflation will reduce purchasing power of a future dollar. D. None of these. 43. Mr. Darden is selling his house for $165,000. He bought it for $55,000 nine years ago. What is the annual return on his investment? A. 3%
B. Between 14% and 16% C. 13% D. None of these 44. Increasing the number of periods will increase all of the following except A. the present value of an annuity. B. the present value of $1. C. the future value of $1. D. the future value of an annuity. 45. Joe Nautilus has $120,000 and wants to retire. What return must his money earn so he may receive annual benefits of $20,000 for the next 14 years. A. 12% B. Between 12% and 13% C. 14% D. Greater than 15% 46. You will deposit $2,000 today. It will grow for 6 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 8%. Your annual withdrawal will be: A. $2,340 B. $4,332 C. $797 D. $1,085 47. Carol Thomas will pay out $6,000 at the end of the year 2, $8,000 at the end of year 3, and receive $10,000 at the end of year 4. With an interest rate of 13 percent, what is the net value of the payments vs. receipts in today's dollars? A. $ 7,326. B. $10,242. C. $16,372. D. $ 4,112. 48. John Doeber borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan in 15 equal annual payments. How much are the annual payments? A. $3,633 B. $9,250 C. $13,113 D. $17,383 49. John Doeber borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan in 15 equal annual payments. What is the principal outstanding after the first loan payment? A. $121,367 B. $123,088 C. $107,617 D. None of these
50. A home buyer signed a 20-year, 8% mortgage for $72,500. How much should the annual loan payments be? A. $1,584 B. $7,384 C. $15,555 D. $15,588 51. After 20 years, 100 shares of stock originally purchased for $1000 was sold for $5,000. What was the yield on the investment? Choose the closest answer. A. 19% B. 5% C. 12% D. 8% 52. The future value of a $1000 investment today at 8 percent annual interest compounded semiannually for 5 years is A. $1,469 B. $1,480 C. $1,520 D. $1,555 53. Dan would like to save $2,000,000 by the time he retires in 40 years and believes he can earn an annual return of 8%. How much does he need to invest today to achieve his goal? A. $136,000 B. $92,000 C. $134,000 D. $625,000 E. $92,060 54. Sydney saved $50,000 during her first year of work after college and plans to invest it for her retirement in 40 years. How much will she have available for retirement if she can make 8% on her investment? A. $596,250 B. $12,953,000 C. $2,345,100 D. $1,086,250
55. Luke believes that he can invest $5,000 per year for his retirement in 30 years. How much will he have available for retirement if he can earn 8% on his investment? A. $566,400 B. $681,550 C. $150,000 D. $162,000 56. Ian would like to save $1,500,000 by the time he retires in 40 years. If he believes that he can achieve a 7% rate of return, how much does he need to deposit
each year to achieve his goal? A. $9,692 B. $37,500 C. $5,790 D. $7,514 57. Jeff believes he will need $60,000 annual income during retirement. If he can achieve a 5% return during retirement and believes he will live 30 years after retirement, how much does he need to save by the time he retires? A. $1,029,540 B. $3,986,340 C. $922,320 D. $259,320 58. If Allison has saved $1,000,000 upon retirement, how much can she live on each year if she can earn 5% per year and will end with $0 when she expects to die 25 years after retirement? A. $295,334 B. $20,953 C. $371,885 D. $70,952 59. Kathy has $60,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years? A. between 7% and 8% B. between 8% and 9% C. between 9% and 10% D. between 10% and 11% 60. If Gerry makes a deposit of $1,500 at the end of each quarter for 5 years, how much will he have at the end of the 5 years assuming a 12% annual return and quarterly compounding? A. $40,305 B. $30,000 C. $108,078 D. $161,220 61. Sara would like to evaluate the performance of her portfolio over the past 5 years. What compound annual rate of return has she achieved is she invested $12,000 5 years ago and now has $25,000? A. between 8% and 9% B. between 10% and 11% C. between 13% and 14% D. between 15% and 16%
