Patricia and Bill want to buy a home and they feel that they

Patricia and Bill want to buy a home, and they feel that they can handle a $1000 per month payment. If they make $1000 payments for 30 years on a 7% APR loan, how much can they borrow?

Solution

We know that the formula for mortgage loans is as under:

M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ – 1]

M is the monthly installment, P is the amount borrowed, i is the monthly interest rate( if APR is quoted, we need to divide by 12) and n = number of payments.

Here, M = $ 1000, i = 7 % = 0.07/12 = 0.005833 ( approx) and n = 30*12 = 360. Then 1000 = P [0.005833(1.005833)³⁶⁰ ] / [ ( 1.005833)³⁶⁰ - 1] or, P = 1000[( 1.005833)³⁶⁰ - 1] / [ 0.005833(1.005833)³⁶⁰] or, P = 1000 ( 8.1155 – 1) / [0.005833(8.1155)] or, P = 1000( 7.1155) / 0.04734 or, P = 7115.5/ 0.04734 = 150306.29 . Thus Patricia and Bill can borrow upto $ 150306.29 pr $150306 ( on rounding off to the nearest Dollar)