The Simpson family plans to buy a new house four years from now for $225,000. Th

Question

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 25 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?

Explanation / Answer

mortagae payment = 57600 * 25% = 14400

so the loan amount is approximately 160970

downpayment = 225000 - 160970 = 64030

future value of savings should be 64030

let x be the monthly deposit

=>

quaterly deposit = 4x

=>

10000 * (1+6%/4)^16 + 4x * [1- (1+6%/4)^-16]/6%/4 = 64030

=>

x = 908.27 (ans)

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