Answer parts (a), (b), and (c) of Exercise 9 if the person takes a 15-year fixed-rate mortgage with a 6% interest rate and intends to pay off the entire loan in 15 years.

Exercise 9

The Federal Housing Finance Board reported that the national average price of a new onefamily house in 2012 was $278,900. At the same time, the average interest rate on a conventional 30-year fixed-rate mortgage was 3.1%. A person purchased a home at the average price, paid a down payment equal to 10% of the purchase price, and financed the remaining balance with a 30-year fixed-rate mortgage. Assume that the person makes payments continuously at a constant annual rate A and that interest is compounded continuously at the rate of 3.1%.

(a) Set up a differential equation that is satisfied by the amount f (t) of money owed on the mortgage at time t.

(b) Determine A, the rate of annual payments that is required to pay off the loan in 30 years. What will the monthly payments be?

(c) Determine the total interest paid during the 30-year term mortgage.