The Simpson family plans to buy a new house four years from

The Simpson family plans to buy a new house four years from now for $225,000. They’ll take out a traditional 25-year mortgage at the time of purchase. Mortgage lenders generally base the amount they will lend on the borrower’s gross family income, allowing roughly 25% of income to be applied to the mortgage payment (for the year). The Simpson’s anticipate that their annual family income will be about $57,600 at the time they will purchase the house. The mortgage interest rate is expected to be about 7.5% at that time and assume that the Simpson family will make the maximum monthly mortgage payment. The mortgage alone won’t provide enough cash to buy the house in 4 years, and the family will need to have a down payment saved to make up the difference. They have a bank account that pays 6% compounded quarterly in which they have already saved $10,000. They plan to make monthly deposits from now until the time of the purchase to save the rest of the down-payment. How much must each monthly deposit be?

Solution

The mortgage payment for the year = 25% * 57600 = 14400 PV of 14400 for 25 years = Formulas $160,516.02 PV(7.5%,25,-14400) The difference to be paid = 225000- 160516 = 64483.98 the value of 10000 in 4 years compounded quarterly $12,689.86 FV(6%/4,16,,-10000) Additional amount = 64483.98-12689.86 = $51,794.12 The amount they have to each quarter is $2,888.30 PMT(6%/4,16,,-A15) Each monthly deposit = 2883.30/3 = 963 Answer: $ 963