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 percent interest rate. How much is in your trust fund today?
2. On January 1, you will purchase a new car. The automobile 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 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 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?