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Time Value of Money

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1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of \$1000, 000 in 12 years. Interest on the trust fund is compounded annually at an 8 percent interest rate. How much is in the trust fund today?

2. On Jan. 1, you will purchase a new car. The car dealer will allow you to make increasing annual Dec. 31 payments over the following four years. The amounts of these payments are \$4,000; \$4,500; \$5,000; \$6,000. On Jan 1, your mother will lend you just enough money to enable you to meet these payments. Interest rates are expected to be 8 percent for the next five years. Assuming that you can earn annual compounding interest by depositing the loan from your mother in a bank, what is the minimum amount your mother must loan you to enable you to meet the car payments?

3. In a settlement of a claim for your recently wrecked car, your insurance company will pay you either a lump sum today or three annual payments of \$3,100 starting one year from now. Interest rates are expected to be 6 percent for the next five years. What is the least amount of money that you should be willing to accept today?

4. What is the present value of \$3,000 a year to be received in years 3 through 11, assuming a 12 percent discount rate?

Solution Preview

1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of \$1000, 000 in 12 years. Interest on the trust fund is compounded annually at an 8 percent interest rate. How much is in the trust fund today?

The future value of the trust fund is given to us. It is 1,000,000. We are to find the present value. The time period is 12 years and the rate is 8%. The PV can be found by using the PVIF table as the amount is a lump sum. From the PVIF table, the factor for 12 years and 8% is 0.397. The PV is 1,000,000X0.397 = \$397,000.
Alternatively we can use the formula.
PV = FV/(1+r)^n
PV = 1,000,000/(1+8%)^12 = 397,114.
The difference due to rounding.

2. On Jan. 1, you will purchase a new car. The car dealer will allow you to make increasing annual Dec. ...

Solution Summary

The solution explains various time value of money questions.

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