You plan to buy a $250,000 home with a 20% down payment. The bank you want to finance the loan through suggests two options: a 15-year mortgage at 4.25% APR and a 30-year mortgage at 5% APR. What is the difference in monthly payments between these two options?

=> The difference of monthly payment between the two options is: $436.4 ( $1,496.5 - $1,060.1) where the monthly payment of the option of 15-year mortgage is higher.

Explanation:

The borrowed amount in both options is : $250,000 * 80% = $200,000;

* A 15-year mortgage monthly payments is:

We have (1+APR) = ( 1 + Monthly Interest rate)^12 <=> 1.0425 = ( 1 + Monthly Interest rate)^12 <=> Monthly Interest rate = 0.3475%;

Amount of payment periods = 15 * 12 = 180

=> Monthly payment = (200,000 * 0.3475%) / [ 1 - 1.003475^(-180) ] = $1,496.5

* A 30-year mortgage monthly payments is:

We have (1+APR) = ( 1 + Monthly Interest rate)^12 <=> 1.05 = ( 1 + Monthly Interest rate)^12 <=> Monthly Interest rate = 0.4074%;

Amount of payment periods = 30 * 12 = 360

=> Monthly payment = (200,000 * 0.4074%) / [ 1 - 1.004074^(-360) ] = $1,060.1