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?