Question

Jack and Jill would like to purchase a house priced at $300,000 with a 30-year mortgage. The bank requires they put a 20% downpayment on the mortgage. The rest of the amount will be provided to J&J by the bank as a loan with 4.25% interest compunded monthly. The initial plan of J&J is to pay off the mortgage on the house in 12x30 = 360 months with equal monthly payments. Calculate the equal end-of-month payments. What is the remaining balance on the loan after 5 years of payments? What is the total amount of the payments that went towards paying the interest portion of the mortgage. J&J decided to make $200 additional payments each month in order to payoff the loan earlier. How long does it take them to payoff the loan now? J&J would like to payoff the loan in 15 years instead of 30 years. How much additional payments should they make each month?

Answer 1

1) Loan amount = 80% * 300,000 = $240,000; loan term = 30 * 12 = 360 months; interest rate = 4.25% p.a.

Using PMT function in excel, PMT = (4.25%/12, 360, -240000) = $1,180.66

Hence, monthly payment required = $1,180.66

Loan table can be set up in excel as below for 360 months:

Month	Opening balance	Interest payment	Principal payment	Closing balance
1	240,000 (=loan amount)	850 (=4.25%*opening balance)	955	239,045
2	239,045 (= closing balance)	847 (=4.25%*opening balance)	959	238,086
3	238,086 (= closing balance)	843 (=4.25%*opening balance)	962	237,123

[Note: Principal payment is calculated as monthly payment of 1,180.66 - interest payment; Closing balance is calculated as Opening balance - Principal payment)

2) Using table above, we can find that balance on the loan after 5 years = $217,938

3) Using table above, we can find that total interest payments = $185,036

4) Using table above, we can find that by paying an additional $200 per month, the loan can be paid off in month 271

5) To pay off the loan in 15 years, monthly payment = $1,805.47 (PMT function in excel)

This implies an additional payment of $624.81