You want to take out a fully-amortizing 30-year mortgage. You can afford monthly payments of $600 each. The interest rate is 9%. How much money can you borrow?

Question

Quizplus · Accepted Answer

The amount of money you can borrow with a fully amortizing loan can be calculated using the formula for the present value of an annuity: $P = \frac{PMT}{r} \left(1 - \frac{1}{(1 + r)^n}\right)$, where $P$ is the loan principal, $PMT$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. Given a monthly payment ($PMT$) of $600, an annual interest rate of 9% (which is 0.09/12 = 0.0075 monthly), and a loan term of 30 years (which is 30*12 = 360 months), the calculation is as follows: $P = \frac{600}{0.0075} \left(1 - \frac{1}{(1 + 0.0075)^{360}}\right)$, which approximately equals $74,569.

You Want to Take Out a Fully-Amortizing 30-Year Mortgage