Question

You take out a mortgage for $290,000. The mortgage carries an APR of 3.75% compounded monthly over 30 years. What is the monthly payment that you would need to make? How much interest do you pay over the life of the loan? If you decide to take a 15-year mortgage instead, you will have a higher monthly payment but you will pay less overall. How much money would you save total vs. the 30-year mortgage?

Answer 1

To find the monthly payment we can use the present value of annuity formula:

Where,
PVA = Present Value of Annuity
A = Annuity / Monthly payments
i = rate of interest
n = number of years
a = number of payments per year
na = Total number of payments

That means monthly payment = $1,343.04

We know total number of payments = 30* 12 = 360

Therefore, total amount paid back in 30 years = $1,343.04 * 360 =  $483,492.68

Therefore, Interest paid over the life of loan =  $483,492.68 - $290,000 = $193,492.68

If the loan is 15-year mortgage instead:

Therefore, if the loan was 15 year mortgage instead then the monthly payments will be $2,108.95

Total payments over the life of the loan = 15 * 12 = 180

Therefore, total amount paid back = $2,108.95 * 180 = $379,610.12

Interest = $379,610.12 - $290,000 =  $89,610.12

Therefore, if you choose 15-year mortgage instead of 30-year then your saving in interest will be :

= $193,492.68 - $89,610.12

= $ 103,882.56