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Sources of Capital; Present Value Concept

For each of the following situations, the present value concept should be applied;

1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of $100,000 in 12 years. Interest on the trust fund is compounded annually at an 8% interest rate. How much is your trust fund today?

2. On January 1, you will purchase a new car. The car dealer will allow you to make increasing annual December 31 payments over the following four years. The amounts of these payments are $4,000, $4,500, $5,000, $6,000. On this same January 1, your mother will lend you just enough money to enable you to meet these payments. Interest rates are expected to be 8% 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 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 3-11, assuming a 12% discount rate?

Solution Preview

For each of the following situations, the present value concept should be applied;

1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of $100,000 in 12 years. Interest on the trust fund is compounded annually at an 8% interest rate. How much is your trust fund today?

PV = FV/(1 + i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period
PV = 100,000/(1.08)12
PV = 39,710

2. On January 1, you will ...

Solution Summary

This solution is comprised of a detailed calculation to calculate how much is your trust fund today, what is the minimum amount your mother must loan you to enable you to meet the car payments, what is the least amount of money that you should be willing to accept today, and what is the present value of #3,000 a year to be received in years 3-11, assuming a 12% discount rate.

$2.19