Question: John is turning 13 today. His birthday resolution is to start saving towards the purchase of a car that he wants to buy on his 18th birthday. The car costs $15,000 today, and he expects the price to grow at 2% per year. John has heard that a local bank offers a savings account which pays an interest rate of 5% per year. He plans to make 6 contributions of $1,000 each to the savings account (the first contribution to be made today); he will use the funds in the account on his 18th birthday as a down payment for the car, financing the balance through the car dealer. He expects the dealer to offer the following terms for financing: 7 equal yearly payments (with the first payment due one year after he takes possession of the car); an annual interest rate of 7%.
a. How much will John need to finance through the dealer?
b. What will be the amount of his yearly payment to the dealer?