Question

Stephen has just purchased a home for ​$. A mortgage company has approved his loan application for a​ 30-year fixed-rate loan at ​%. Stephen has agreed to pay ​% of the purchase price as a down payment. How much would​ Stephen's monthly payment increase for a​ 20-year mortgage over a​ 30-year mortgage?

Answer 1

To calculate the monthly payment for a mortgage, use the mortgage payment formula: PMT = P*(r*((1+r)^n))/(((1+r)^n)-1). Calculate the monthly payments for both a 20-year mortgage and a 30-year mortgage using this formula. Then, find the difference in the payments.

Step-by-step explanation:

To calculate the monthly payment for a mortgage, we can use a formula known as the mortgage payment formula. This formula is given by:

PMT = P*(r*((1+r)^n))/(((1+r)^n)-1)

Where:

PMT: Monthly payment

P: Loan amount

r: Monthly interest rate (annual interest rate divided by 12)

n: Total number of payments

In this case, Stephen has agreed to pay a certain percentage of the purchase price as a down payment. Let's say the purchase price is $X and he is paying Y% of it as a down payment. Then, the loan amount (P) is given by $X - (Y/100)*$X.

To compare the monthly payment for a 20-year mortgage and a 30-year mortgage, we need to calculate the monthly payments using the mortgage payment formula for both cases and then find the difference in the payments.