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Principles Of Fianance: Homework Chapter 4 Homework 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 | Exam 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | Final Exam 1 2 For each of the following, compute the future value: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Explanation: To find the FV of a lump sum, we use: FV = PV(1 + r)t
For each of the following, compute the present value: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Explanation: To find the PV of a lump sum, we use: PV = FV / (1 + r)t
Solve for the unknown interest rate in each of the following: (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Explanation: To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t – 1
FV = $1,501 = $775(1 + r)6 r = ($1,501 / $775)1/6 – 1 r = .1165, or 11.65%
FV = $1,838 = $965(1 + r)7 r = ($1,838 / $965)1/7 – 1 r = .0964, or 9.64%
FV = $147,832 = $21,000(1 + r)18 r = ($147,832 / $21,000)1/18 – 1 r = .1145, or 11.45%
FV = $324,815 = $76,300(1 + r)21 r = ($324,815 / $76,300)1/21 – 1 r = .0714, or 7.14% Solve for the unknown number of years in each of the following: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Explanation: To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r)
FV = $1,155 = $300(1.10)t t = ln($1,155 / $300) / ln1.10 t = 14.14 years
FV = $3,750 = $1,991(1.08)t t = ln($3,750 / $1,991) / ln1.08 t = 8.23 years
FV = $387,620 = $32,905(1.13)t t = ln($387,620 / $32,905) / ln1.13 t = 20.18 years
FV = $199,724 = $32,600(1.20)t t = ln($199,724 / $32,600) / ln1.20 t = 9.94 years Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. Present Value Years Interest Rate Future Value $ 2,597 11 13% ? $ 7,834 7 9% ? $ 81,286 14 12% ? $ 213,612 16 6% ? $ 9,961.73 $ 14,320.86 $ 397,253.81 $ 542,649.60 First City Bank pays 7.5 percent simple interest on its savings account balances, whereas Second City Bank pays 7.5 percent interest compounded annually. If you made a deposit of $8,600 in each bank, how much more money would you earn from your Second City Bank account at the end of eight years? $1,577.90 Simple interest you will earn: $8,600 * 7.5% * 8 = $5,160 Compound interest you will earn: $8, 600 * (1 + 0. 075)^8 = 15,337.909 Interest gained = 15,337.909 - $8,600 = $6,737.909 You will earn ($1,577.909) more money from second city bank: $6,737.909 - $5,160 = $1,577.90 If you believe your mutual fund can achieve an annual rate of return of 8.2 percent and you want to buy the car in 9 years (on the day you turn 30), how much must you invest today? $124,879.43 $101,930.18 $98,876.42 $119,221.99 $130,376.86 Future Value Interest rate Annuity Payments Time period $1,440 $3,079 $3,849 $1,849 $1,200 Assume you earn a return of 14 percent per year and make no additional contributions. a. What will your account be worth when you retire in 25 years? b. What if you wait 10 years before contributing? $105,847.66 $28,551.75 The bank pays 5.8 percent annual interest on its accounts. How long will it be before you have enough to buy the car? 24.59 years Time period Free Cash Flow Present Value Interest rate $397 $1,586 $1,000 $837 $1,386 Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Switzers's sold the Mayfield Escape gold sculpture Champion, I Wish at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $13,377,500. What was his annual rate of return on this sculpture? -6.30% 4.78% -2.89% 5.12% -4.46% You have just received notification that you have won the $3 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 78 years from now. What is the present value of your windfall if the appropriate discount rate is 10 percent? $1,772.11 How much should she put into her savings account today in order to have enough for this vacation? 5,196.72 6500 / (1 + .038)6 = 5,196.719018 Zach and Kim want to begin saving for their daughter's college education. They have estimated that she will need $150,000 in 17 years. If they feel confident that you can earn 8% per year, how much do they need to invest today? $40,540.34 150,000 / (1 + .08)17 Present Value (One Period) - Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today? $9,345.79 10,000 / (1 + .07)1 How much will be in Fran's account after 8 years? $36,552.09 30,000 (1 + .025)8 Suppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years. If you currently sell 3 million widgets in one year, how many widgets do you expect to sell in 5 years? 6,034,072 3,000,000(1 + .15)5 You have just made your first $5,500 contribution to your retirement account. Assume you earn a return of 10 percent per year and make no additional contributions. a. What will your account be worth when you retire in 45 years? b. What if you wait 10 years before contributing? a: Future Value for starting now: $400,897.66 b: Future value if waiting 10 years: $154,563.40 5500(1.10)45 5500(1.10)35 If you believe your mutual fund can achieve an annual rate of return of 11.2 percent and you want to buy the car in 9 years (on the day you turn 30), how much must you invest today? Investment: $105,776.60 275,000(1.112)8 The “Brasher doubloon,” which was featured in the plot of the Raymond Chandler novel, The High Window, was sold at auction in 2018 for $5.5 million. The coin had a face value of $15 when it was first issued in 1787 and had been previously sold for $430,000 in 1979. a. At what annual rate of return did the coin appreciate from its minting to the 1979 sale? b. What annual rate of return did the 1979 buyer earn on his purchase? c. At what annual rate of return did the coin appreciate from its minting to the 2014 sale? a: Rate of Return = 5.49% b: Rate of Return = 6.75% c: Rate of Return = 5.70% Your coin collection contains fifty 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2067, assuming they appreciate at an annual rate of 4.3 percent? Future Value: $6,333.82 2067 – 1952 = 115 50(1.043)115 However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 9.1 percent? Present Value: $1,883.87 2,000,000(1.091)80 Imprudential, Incorporated, has an unfunded pension liability of $450 million that must be paid in 20 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.2 percent, what is the present value of this liability? Present Value: $163,266,738.60 You're trying to save to buy a new $275,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 4.8 percent annual interest on its accounts. How long will it be before you have enough to buy the car? It will take 36.36 years. 275,000 / 50,000 = 5.5 4.8% = 0.048 1 + 0.048 = 1.048 log(5.5) / log(1.048) = 36.36129915 When the future value formula is used to calculate growth rates, the assumption is that _____ growth rate is achieved each year. A: different B: regressing C: the same D: stair-stepped What is the future value of $100 compounded for 50 years at 10 percent annual interest? A: $14,987.45 B: $500.00 C: $11,739.09 D: $868.85 C: $11,739.09 If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years? A: $130.00 B: $133.10 C: $131.00 D: $121.00 100 x (1 + 0.1)3 Which formula below represents a present value factor? A: 1/N + 1/r B: (1 + r)/t C: 1/(1 + N)r D: 1/(1 + r)t Future value is the ________ value of an investment at some time in the future. A: cash B: indirect C: relational D: interest A: $120.00 B: $110.00 C: $100.00 D: $121.00 _____ value is the cash value of an investment at some time in the _______. Future, future. The sales quote consists of quarterly payments of $37,200 for five years at 7.6 percent interest. What is the purchase price? A. $621,380.92 B. $614,184.40 C. $687,418.22 D. $774,311.28 E. $836,267.35 37,200 × (1 - {1 / [1 + (.076 / 4)]20}) / (.076 / 4) = $614,184.40 Today, you are purchasing a 20-year, 6 percent annuity at a cost of $48,350. The annuity will pay annual payments starting one year from today. What is the amount of each payment? A. $4,511.08 B. $4,215.37 C. $2,754.40 D. $4,013.20 E. $5,208.19 48,350 = C × {1 - [1 / (1 + .06)20]} / .06 C = 4,215.37 You will receive annual payments of $800 at the end of each year for 12 years. The first payment will be received in Year 3. What is the present value of these payments if the discount rate is 7 percent? A. $5,465.20 B. $6,018.52 C. $6,299.80 D. $5,549.96 E. $6,856.60 PV2 = 800 × ({1 - [1 / (1 + .07)12]} / .07) × (1 + .07) = 6,354.15 PV0 = 6,354.15 / (1 + .07)2 = 5,549.96 You want to purchase a new condominium that costs $287,500. Your plan is to pay 25 percent down in cash and finance the balance over 15 years at 3.75 percent. What will be your monthly mortgage payment including principal and interest? A. $1,568.07 B. $1,333.33 C. $1,708.16 D. $1,221.43 E. $1,406.11 (1 - .25) × 287,500 = 215,625 215,625 = C × (1 - {1 / [1 + (.0375 / 12) x 180 / (.0375 / 12) C = 1,568.07 What is the effective annual rate of 8.25 percent compounded quarterly? A. 8.25 percent B. 8.49 percent C. 8.38 percent D. 8.51 percent E. 8.56 percent [1 + (.0825 /4)]4 - 1 = .0851, or 8.51 percent Capstone Investments is considering a project that will produce cash inflows of $11,000 at the end of Year 1, $24,000 in Year 2, and $36,000 in Year 3. What is the present value of these cash inflows at a discount rate of 12 percent? $54,578.17 PV = (11,000 / 1.12) + (24,000 / 1.1222) + (36,000 / 1.1233) = 54,578.17 ST Trucking just signed a $3.8 million contract. The contract calls for a payment of $1.1 million today, $1.3 million one year from today, and $1.4 million two years from today. What is this contract worth today at a discount rate of 8.7 percent? $3,480,817.37 1.1m + (1.3m/1.087) + ($1.4m/1.0872) = 3,480,817.37 Eric is considering an investment that will pay $8,200 a year for five years, starting one year from today. What is the maximum amount he should pay for this investment if he desires a rate of return of 11.2 percent? $30,154.50 8,200 ×{1 - [1 / (1 + .112)5]} / .112 = 30,154.50 How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $42,000 a year for 25 years? She expects to earn an average rate of return of 9.75 percent. 388,683.83 42,000 × {1 - [1 / (1 + .0975)25]} / .0975 = 388,683.83 Which one of the following statements concerning annuities is correct? A. The present value of an annuity is equal to the cash flow amount divided by the discount rate. B. An annuity due has payments that occur at the beginning of each time period. C. The future value of an annuity decreases as the interest rate increases. D. If unspecified, you should assume an annuity is an annuity due. E. An annuity is an unending stream of equal payments occurring at equal intervals of time. Suenette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the end of Year 3. If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3? A. $2,200.00 B. $2,238.47 C. $2,468.69 D. $2,309.16 E. $2,402.19 Western Bank pays 5 percent simple interest on its savings account balances, whereas Eastern Bank pays 5 percent compounded annually. If you deposited $6,000 in each bank, how much more money would you earn from the Eastern Bank account at the end of 3 years? A) $55.84 B) $45.75 C) $60.47 D) $40.09 E) $50.14 Assume the total cost of a college education will be $325,000 when your child enters college in 16 years. You presently have $40,000 to invest and do not plan to invest anything further. What annual rate of interest must you earn on your investment to cover the entire cost of your child's college education? A) 12.65 percent B) 10.40 percent C) 13.99 percent D) 14.62 percent E) 11.08 percent At 10 percent interest, how long does it take to triple your money? A) 14.33 years B) 11.53 years C) 9.67 years D) 10.36 years E) 10.56 years You're trying to save to buy a new car valued at $42,650. You have $40,000 today that can be invested at your bank. The bank pays 4.2 percent annual interest on its accounts. How long will it be before you have enough to buy the car for cash? Assume the price of the car remains constant. A) 1.17 years B) 2.12 years C) 1.06 years D) 1.61 years E) 1.56 years Your coin collection contains ten 1949 silver dollars. If your grandparents purchased the coins for their face value when they were new, how much will your collection be worth when you retire in 2065, assuming the coins appreciate at an annual rate of 5.1 percent? A) $3,440.63 B) $2,329.29 C) $3,348.98 D) $3,205.64 E) $2,644.29 Suppose that in 2015, a $10 silver certificate from 1898 sold for $11,700. For this to have been true, what would the annual increase in the value of the certificate have been? A) 6.22 percent B) 6.01 percent C) 7.23 percent D) 6.49 percent E) 7.07 percent You have just made your first $5,000 contribution to your retirement account. Assuming you earn a rate of return of 5 percent and make no additional contributions, what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing? A) $26,335.37; $23,011.60 B) $27,311.20; $29,803.04 C) $27,311.20; $22,614.08 D) $27,580.08; $21,609.71 E) $31,241.90; $32,614.08 You are scheduled to receive $5,000 in two years. When you receive it, you will invest it at 6.5 percent per year. How much will your investment be worth eight years from now? A) $7,295.71 B) $8,274.98 C) $6,850.43 D) $10,665.75 E) $7,302.27 You expect to receive $5,000 at graduation one year from now. Your plan is to invest this money at 6.5 percent, compounded annually, until you have $50,000. At that time, you plan to travel around the world. How long from now will it be until you can begin your travels? A) 36.57 years B) 31.08 years C) 34.55 years D) 32.08 years E) 37.57 years Homework 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 | Exam 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | Final Exam 1 2
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