Question

A lender requires that monthly mortgage payments be no more than 25% of gross monthly income with a maximum termof 30 years. If you can make only a 15% down payment, what is the minimum monthly income needed to purchase a $300,000 house when the interest rate is 6% compounded monthly?

Answer 1

Answer:

$61,187.6

Explanation:

We first, must find the value of the monthly payments. Because the payments are regular in time, have the same value, and fall under the same interest rate, the payments are an annuity.

To find the value of the monthly payments, we use the present value of an annuity formula, but first, we substract the down payment from the total mortgage payment (300,000 x 15% = 45,000), so the mortgage payment that we will use in the formula is = 300,000 - 45,000 = 255,000

$255,000 = X ((1-(1+0.06)^{-360} )/0.06)\\255,000 = X (16.67)\\\\\frac{255,000}{16.67} = X\\\\15,296.9 = X$

Because the lender requires the monthly payments to be no more than 25% of gross income, we need to find for what value $15,296.9 is the 25% of:

15,296.9 x 100 / 25 = 61,187.6