Problems

1. I am borrowing $15,000 to buy a new car. I am going to make 60 end-of-month payments. The annual interest rate on the loan is 10 percent. The car dealer is a friend of mine, and he will allow me to make the monthly payment for Months 1–30 equal to onehalf the payment for Months 31–60. What is the payment during each month?

2. Solve the retirement planning problem assuming that withdrawals occur at the end of each year and contributions occur at the beginning of each year.

3. Solve our mortgage example assuming that payments are made at the beginning of each month.

4. In the retirement-planning example, suppose that during Year 1, our salary is $40,000 and our salary increases 5 percent per year until retirement. We want to save the same percentage of our salary each year we work. What percentage of our salary should we save?

5. In the mortgage example, suppose that we want our monthly payment to increase by $50 each month. What should each month’s payment be?

6. Assume we want to take out a $300,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 6 percent. Twenty years from now, we need to make an ending balloon payment of $40,000. Because we expect our income to increase, we want to structure our loan so at the beginning of each year our monthly payments increase by 2 percent. Determine the amount of each year’s monthly payment.