Question

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 the 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?