Question

You plan to purchase a $300,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 7.80 percent, or a 20-year mortgage with a rate of 7.20 percent. You will make a down payment of 15 percent of the purchase price. a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid? b. Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages?

Answer 1

30 year mortgage:
Monthly payment=PMT(7.8%/12,12*30,-300000*(1-15%))=$1,835.67
Amount of interest paid=1835.67*12*30-300000*(1-15%)=405841.2

20 year mortgage:
Monthly payment=PMT(7.2%/12,12*20,-300000*(1-15%))=$2,007.74
Amount of interest paid=2007.74*12*20-300000*(1-15%)=226857.6

Amount of principal paid will be equal to 300000*(1-15%)=255000 in both the cases
Difference in interest paid=405841.2-226857.6=178983.6
Difference in monthly payment=2007.74-1835.67=$172.07