Question

A woman buys a house for a ​$320000. She pays ​$40000 down and takes out a mortgage at 5.7​% for 20 years on the balance. Find her monthly payment and the total amount of interest she will pay. The woman will make payments of ​$ nothing.

Answer 1

Answer:

$PMT= 1957.850$

Explanation:

For this case the total payment is $320000, and she pays $40000 so the remain amount to pay would be:

$320000-40000=$ 280000

For this case we assume that the annual interest rate is APR=5.7% =0.057 on fraction.

The total number of years are 20. For this case n represent the number of payments per year and since we have monthly payments then n =12.

In order to find the PMT we can use the following formula:

$PMT= \frac{P(\frac{APR}{n})}{[1-(1+\frac{APR}{n})^{-nt}]}$

On the last expression the APR needs to be on fraction and P represent the principal amount, for this case P = $280000. So if we replace we got:

$PMT= \frac{280000(\frac{0.057}{12})}{[1-(1+\frac{0.057}{12})^{-12*20}]}$

$PMT= 1957.850$

And we can verify this using the following excel function: "=PMT(0.057/12,12*20,-280000)"