Q&A Hero

Q: Your bank offers a savings account that pays 3.5% interest, compounded annually. How much will $500 invested today be worth at the end of 25 years? a. $1,122.54 b. $1,181.62 c. $1,240.70 d. $1,302.74 e. $1,367.88

Q: How much would $100, growing at 5% per year, be worth after 75 years? a. $3,689.11 b. $3,883.27 c. $4,077.43 d. $4,281.30 e. $4,495.37

Q: Cochrane Associate's net sales last year were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later? a. $845.03 b. $889.51 c. $936.33 d. $983.14 e. $1,032.30

Q: Cyberhost Corporation's sales were $225 million last year. If sales grow at 6% per year, how large (in millions) will they be 5 years later? a. $271.74 b. $286.05 c. $301.10 d. $316.16 e. $331.96

Q: Your bank offers a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. If you invest $2,000 in the CD, how much will you have when it matures? a. $3,754.27 b. $3,941.99 c. $4,139.09 d. $4,346.04 e. $4,563.34

Q: JG Asset Services is recommending that you invest $1,500 in a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures? a. $1,781.53 b. $1,870.61 c. $1,964.14 d. $2,062.34 e. $2,165.46

Q: How much would Roderick have after 6 years if he has $500 now and leaves it invested at 5.5% with annual compounding? a. $591.09 b. $622.20 c. $654.95 d. $689.42 e. $723.89

Q: Ellen now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding? a. $205.83 b. $216.67 c. $228.07 d. $240.08 e. $252.08

Q: Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) a. True b. False

Q: Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) a. True b. False

Q: The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date. a. True b. False

Q: Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts. a. True b. False

Q: Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods. a. True b. False

Q: Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. a. True b. False

Q: Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. a. True b. False

Q: Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly. a. True b. False

Q: A time line is not meaningful unless all cash flows occur annually. a. True b. False

Q: A time line is meaningful even if all cash flows do not occur annually. a. True b. False

Q: Starting to invest early for retirement reduces the benefits of compound interest. a. True b. False

Q: Starting to invest early for retirement increases the benefits of compound interest. a. True b. False

Q: You are in negotiations to make a 7-year loan of $25,000 to DeVille Corporation. To repay you, DeVille will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. You are confident the payments will be made, since DeVille is essentially riskless. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X? a. $4,271.67 b. $4,496.49 c. $4,733.15 d. $4,969.81 e. $5,218.30

Q: Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age. Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday? a. $3,726 b. $3,912 c. $4,107 d. $4,313 e. $4,528

Q: Your older brother turned 35 today, and he is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year. a. $58,601 b. $61,686 c. $64,932 d. $68,179 e. $71,588

Q: The store where you bought new home furnishings offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan? a. 12.31% b. 12.96% c. 13.64% d. 14.36% e. 15.08%

Q: You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000? a. 39.60 b. 44.00 c. 48.40 d. 53.24 e. 58.57

Q: You are considering investing in a European bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up. a. 23 b. 27 c. 32 d. 38 e. 44

Q: Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days? a. $5,178.09 b. $5,436.99 c. $5,708.84 d. $5,994.28 e. $6,294.00

Q: Billy Thornton borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Billy have to pay in a 30-day month? a. $120.83 b. $126.88 c. $133.22 d. $139.88 e. $146.87

Q: At a rate of 6.5%, what is the future value of the following cash flow stream? a. $526.01 b. $553.69 c. $582.83 d. $613.51 e. $645.80

Q: You sold your motorcycle and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? a. $5,987 b. $6,286 c. $6,600 d. $6,930 e. $7,277

Q: What is the present value of the following cash flow stream at a rate of 8.0%? a. $7,917 b. $8,333 c. $8,772 d. $9,233 e. $9,695

Q: What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250? a. $77.19 b. $81.25 c. $85.31 d. $89.58 e. $94.06

Q: A perpetuity pays $85 per year and costs $950. What is the rate of return? a. 8.95% b. 9.39% c. 9.86% d. 10.36% e. 10.88%

Q: What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%? a. $4,750 b. $5,000 c. $5,250 d. $5,513 e. $5,788

Q: You plan to work for Strickland Corporation for 12 years after graduation and after that want to start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandmother just gave you a $25,000 graduation gift that you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now? a. $238,176 b. $250,712 c. $263,907 d. $277,797 e. $291,687

Q: You want to open a sushi bar 3 years from now, and you plan to save $7,000 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today? a. $20,993 b. $22,098 c. $23,261 d. $24,424 e. $25,645

Q: You want to purchase a motorcycle 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today? a. $16,112 b. $16,918 c. $17,763 d. $18,652 e. $19,584

Q: You would like to travel in South America 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now? a. $18,369 b. $19,287 c. $20,251 d. $21,264 e. $22,327

Q: You want to buy new kitchen appliances 2 years from now, and you plan to save $8,200 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now? a. $15,260 b. $16,063 c. $16,908 d. $17,754 e. $18,642

Q: You are hoping to buy a new boat 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now? a. $11,973 b. $12,603 c. $13,267 d. $13,930 e. $14,626

Q: Your investment advisor has recommended your invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000? a. 12.37 b. 13.74 c. 15.27 d. 16.97 e. 18.85

Q: Your investment account pays 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? a. 5.14 b. 5.71 c. 6.35 d. 7.05 e. 7.84

Q: Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Brockman's EPS to triple? a. 9.29 b. 10.33 c. 11.47 d. 12.75 e. 14.02

Q: Your bank pays 4% interest annually. You have $2,500 invested in the bank. How long will it take for your funds to double? a. 14.39 b. 15.15 c. 15.95 d. 16.79 e. 17.67

Q: You have $5,000 invested in a bank that pays 3.8% annually. How long will it take for your funds to triple? a. 23.99 b. 25.26 c. 26.58 d. 27.98 e. 29.46

Q: Wildwoods, Inc. earned $1.50 per share five years ago. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period? a. 15.54% b. 16.36% c. 17.18% d. 18.04% e. 18.94%

Q: Ten years ago, Kronan Corporation earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in earnings per share (EPS) over the 10-year period? a. 15.17% b. 15.97% c. 16.77% d. 17.61% e. 18.49%

Q: You have purchased a U.S. Treasury bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate will you earn on this bond? a. 3.82% b. 4.25% c. 4.72% d. 5.24% e. 5.77%

Q: You have just purchased a U.S. Treasury bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate will you earn on this bond? a. 4.37% b. 4.86% c. 5.40% d. 6.00% e. 6.60%

Q: You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset? a. 4.93% b. 5.19% c. 5.46% d. 5.75% e. 6.05%

Q: Your sister paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment? a. 6.77% b. 7.13% c. 7.50% d. 7.88% e. 8.27%

Q: Which of the following statements is CORRECT? a. If CF0 is positive and all the other CFs are negative, then you can still solve for I. b. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0. c. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost. d. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator. e. If you solve for I and get a negative number, then you must have made a mistake.

Q: Which of the following statements is CORRECT? a. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. b. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. c. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. d. The cash flows for an annuity due must all occur at the beginning of the periods. e. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.

Q: You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning? a. 7.62% b. 8.00% c. 8.40% d. 8.82% e. 9.26%

Q: Your Green Investment Tips subscription is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? a. 7.48 b. 8.80 c. 10.35 d. 12.18 e. 14.33

Q: Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to open a new restaurant, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment? a. 6.85% b. 7.21% c. 7.59% d. 7.99% e. 8.41%

Q: Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity? a. 3.44% b. 3.79% c. 4.17% d. 4.58% e. 5.04%

Q: Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes. a. 7.12% b. 7.49% c. 7.87% d. 8.26% e. 8.67%

Q: Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. When she makes her last withdrawal (at the beginning of a year), she also wants to have enough left in the account so that you can make a final withdrawal of $50,000 at the end of that year (her last withdrawal is at the beginning of the year, your withdrawal is at the end of that same year). What is the maximum number of $45,000 withdrawals that she can make and still have enough in the account so that you can make a $50,000 withdrawal at the end of the year of her last withdrawal? (Hint: If your solution for N is not an integer, round down to the nearest whole number.) a. 13 b. 14 c. 15 d. 16 e. 17

Q: Your Aunt Elsa has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.) a. 18 b. 19 c. 20 d. 21 e. 22

Q: Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.) a. 12 b. 13 c. 14 d. 15 e. 16

Q: Your uncle just won the weekly lottery, receiving $375,000, which he invested at a 7.5% annual rate. He now has decided to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.) a. 22 b. 23 c. 24 d. 25 e. 26

Q: Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years? a. $22,598.63 b. $23,788.03 c. $25,040.03 d. $26,357.92 e. $27,675.82

Q: You were left $100,000 in a trust fund set up by your grandfather. The fund pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account? a. $24,736 b. $26,038 c. $27,409 d. $28,779 e. $30,218

Q: Your aunt wants to retire and has $375,000. She expects to live for another 25 years, and she also expects to earn 7.5% on her invested funds. How much could she withdraw at the beginning of each of the next 25 years and end up with zero in the account? a. $28,243.21 b. $29,729.70 c. $31,294.42 d. $32,859.14 e. $34,502.10

Q: Suppose you earned a $275,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years? a. $28,532 b. $29,959 c. $31,457 d. $33,030 e. $34,681

Q: Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.

Q: Which of the following statements is CORRECT? a. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity. b. A time line is not meaningful unless all cash flows occur annually. c. Time lines are not useful for visualizing complex problems prior to doing actual calculations. d. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. e. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.

Q: Which of the following statements is CORRECT? a. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. b. A time line is not meaningful unless all cash flows occur annually. c. Time lines are not useful for visualizing complex problems prior to doing actual calculations. d. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. e. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

Q: Your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for for the first year of the loan? (Assume she took out the loan on January 1.) a. $17,419.55 b. $17,593.75 c. $17,769.68 d. $17,947.38 e. $18,126.85

Q: Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal? a. 73.67% b. 77.55% c. 81.63% d. 85.93% e. 90.45%

Q: Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment? a. $10,155.68 b. $10,690.19 c. $11,252.83 d. $11,845.09 e. $12,468.51

Q: Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2? a. $7,531 b. $7,927 c. $8,323 d. $8,740 e. $9,177

Q: You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2? a. $1,994.49 b. $2,099.46 c. $2,209.96 d. $2,326.27 e. $2,442.59

Q: Your cousin will sell you his coffee shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be? a. $4,029.37 b. $4,241.44 c. $4,464.67 d. $4,699.66 e. $4,947.01

Q: Suppose you are buying your first home for $145,000, and you have $15,000 for your down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be? a. $741.57 b. $780.60 c. $821.69 d. $862.77 e. $905.91

Q: Which of the following statements regarding a 20-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? a. Exactly 10% of the first monthly payment represents interest. b. The monthly payments will increase over time. c. A larger proportion of the first monthly payment will be interest, and a smaller proportion will be principal, than for the last monthly payment. d. The total dollar amount of interest being paid off each month gets larger as the loan approaches maturity. e. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.

Q: Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) a. The outstanding balance declines at a faster rate in the later years of the loan's life. b. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. c. Because the outstanding balance declines over time, the monthly payments will also decline over time. d. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. e. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.

Q: A $150,000 loan is to be amortized over 6 years, with annual end-of-year payments. Which of these statements is CORRECT? a. The proportion of interest versus principal repayment would be the same for each of the 7 payments. b. The annual payments would be larger if the interest rate were lower. c. If the loan were amortized over 10 years rather than 6 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 6-year amortization plan. d. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower. e. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher.

Q: Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate. a. True b. False