ASSIGNMENT
1. 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 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 cannot be constructed for annuities where the payments occur at the beginning of the periods.
2. 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
3. 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
4. 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
5. 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
6. What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?
A. $16,576
B. $17,449
C. $18,367
D. $19,334
E. $20,352
7. Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
A. $5,493.71
B. $5,782.85
C. $6,087.21
D. $6,407.59
E. $6,744.83
8. After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it in an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
A. $50,753
B. $53,424
C. $56,236
D. $59,195
E. $62,311
9. An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him with income of $50,000 per year for 30 years, beginning a year from today (one year from today). The going rate on such annuities is 7.25%. How much would it cost him to buy such an annuity today?
A. $574,924
B. $605,183
C. $635,442
D. $667,214
E. $700,575
10. 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
11. A new investment opportunity for you is an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
A. $1,412.84
B. $1,487.20
C. $1,565.48
D. $1,643.75
E. $1,725.94
12. A salt mine you inherited will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the mine is 7.5%, how much should you ask for it if you decide to sell it?
A. $284,595
B. $299,574
C. $314,553
D. $330,281
E. $346,795
13. What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?
A. $8,509
B. $8,957
C. $9,428
D. $9,924
E. $10,446
14. 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? Hint: First payment today.
A. $28,243.21
B. $29,729.70
C. $31,294.42
D. $32,859.14
E. $34,502.10
15. 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.) Hint: First payment one year from today.
A. 22
B. 23
C. 24
D. 25
E. 26
16. 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
17. 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%? Hint: What is the PV of these cash flows.
A. $5,987
B. $6,286
C. $6,600
D. $6,930
E. $7,277
18. 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%
19. What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
A. $3,089
B. $3,251
C. $3,422
D. $3,602
E. $3,782
20. Southwestern Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Woodburn Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Woodburn versus the rate charged by Southwestern? Hint: Simply compare effective rates.
A. 0.52%
B 0.44%
C. 0.36%
D. 0.30%
E. 0.24%
21. 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
22. 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 (ordinary annuity), 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
23. 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? Hint: First, find payment and the use Amort function.
A. $1,994.49
B. $2,099.46
C. $2,209.96
D. $2,326.27
E. $2,442.59
24. 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. Hint: First payment today.
A. 23
B. 27
C. 32
D. 38
E. 44
25. 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 (last deposit on Year 65). 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 (that is in Year 66) and last withdrawal will be in Year 90.
A. $58,601
B. $61,686
C. $64,932
D. $68,179
E. $71,588
26. 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%
27. Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return (nominal rate). If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living? Hint: First, find real rate of return, using Real rate= {(1+nominal)/(1+inflation rate)} - 1, and then find payment by setting payment to BEG (first payment today).
A. $65,632
B. $72,925
C. $81,027
D. $89,130
E. $98,043
28. 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
29. 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
30. Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years - if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). Hint: You will be using growth rates of tuition as i/y and find the different tuition for these years.
So far, Scott and Linda have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Casie's anticipated college costs?
A. $1,965.21
B. $2,068.64
C. $2,177.51
D. $2,292.12
E. $2,412.76