time value of money problems

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Time Value of Money Problems

8. Calculating Interest rates You are offered an investment that requires you to put up $4,000 today in exchange for $10,000 eight years from now. What is the rate of return on this investment?

Answer:12.14%

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9.Calculating the Number of Periods You’re trying to save to

buy a new $20,000 speedboat to take to the lake. You have

$16,000 today that can be invested at your bank. The bank pays 6

percent annual interest on its accounts. How long will it be before

you have enough to buy the speedboat?

Answer: 3.83 years

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11. Present Value and Multiple Cash Flows Looking Good Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 14 percent?

Answer: @10% 1,688.71@14% 1,559.83

Year Cash Flow 1 $500 2 $700 3 $600 4 $300

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16. Calculating Annuity Values Your company will generate$27,000 annual payments each year for the next eight years

from a new information database. The computer system needed to

set up the data base costs $180,000. If you can borrow the money

to buy the computer system at 7 percent annual interest, can you afford the new system?

Answer: 161,225.1<180,000 can’t afford it

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18. Annuity Values You want to have $17,000 in your savings

account six years from now, and you are prepared to make equal

annual deposits into the account at the end of each year. If the

account pays 8 percent interest, what amount must you deposit

each year?

Answer: 2,317.37

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20. Perpetuity Values Bob’s Life Insurance Co. is trying to sell

you an investment policy that will pay you and your heirs $700 per

year forever. If the required return on this investment is 12 percent, how much will you pay for the policy?

Answer: 5,833.33

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22. Calculating EAR Find the EAR in each of the cases below.

Answer: 10.38% 17.23% 9.42% 23.37%

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23. Calculating APR Find the APR or stated rate in each of the cases below.

Answer: 7.85%11.39%15.72%21.57%

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28. Calculating Present Value An investment will pay you

$34,000 in four years. If the appropriate discount rate is 11 percent compounded daily, what is the present value?

Answer: 21,895.52

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32. Calculating EAR Rocko’s Quick Loans, Inc. offers you ”three

for four or I knock on your door”. This means you get $3 today from Rocko and repay him $4 when you get your paycheck in 5 days (or else) What’s the effective annual return Rocko earns on this lending business? If you’re brave enough to ask him, what

APR would Rocko say you’re paying?

Answer: EAR 131,985,971,000%APR 2,433.33%

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33. Valuing Perpetuities Lollapalooza Life Insurance Co. is selling a

perpetual annuity contract that pays $500 monthly. The contract

currently sells for $60,000. What is the monthly return on this

investment vehicle? What is the APR? The effective annual return?

Answer: monthly return 0.833%APR 10%EAR 10.47%

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47. Calculating Loan Payments You need a 15-year, fixed-rate

mortgage to buy a new home for $80,000. Your mortgage bank will lend you the money at an 8.5 percent APR for this 180-month loan. However, you can only afford monthly payments of $395,

so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments?

Answer: 142,106.65 note: the effect of rounding may be quite big

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48. EAR versus APR You have just purchased a new warehouse.

To finance the purchase, you’ve arranged for a 20-year mortgage

loan for 90 percent of the $700,000 purchase price. The monthly

payment on this loan will be $5,500. What is the APR on this loan?

The EAR?

Answer: APR 8.582%EAR 8.93%

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55. Present Value of a Perpetuity Given an interest rate of 6.6

percent per year, what is the value at date t=9 of a perpetual

stream of $300 payments that begin at date t=14.

Answer: 3,520.04

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56. Calculating EAR A local finance company quotes a 23 percent interest rate on one year loans. So if you borrow $10,000, the interest for the year will be $2,300. Since you must repay a total of $12,300 in one year, the finance company requires you to pay $12,300/12 or $1,025 per month over the next 12 months. Is this a 23 percent loan? What rate would legally have to be

quoted? What is the effective annual rate?

Answer: APR 40.08%EAR 48.33%

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66. Calculating Annuity Payments This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $15,000 from her savings account on each birthday for 12 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 9 percent interest per year. She wants to make equal, annual payments on each birthday into the account established at the credit union for her retirementfund.a. If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65(the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement.

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b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump-sum payment on her 36th birthday to cover her retirement needs. What amount would she have to deposit?

c. Suppose your friend’s employer will contribute $250 into the account every year as part of the company’s profit-sharing plan. In addition, your friend expects a $10,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?Answer: 788.0

8,824.3364.3

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68. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the followingsix payments to the insurance company:

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $120,000. If the relevant interest rate is 8 percent for the six years and 5 percent for all subsequent years,is the policy worth buying?Answer: 144,942.12>120,000 don’t buy it

1st birthday $1,000 2nd birthday $1,000 3rd birthday $1,000 4th birthday $1,250 5th birthday $1,250 6th birthday $1,250

time value of money problems

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