John is purchasing a house for $500,000. He plans to make a down payment of $100,000 and take out a 30-year mortgage for $400,000. a. If the interest rate on the house is 5.5 per cent per year, how much will his monthlypayment be for principal and interest? b. If the interest rate is the same, how much would his monthlypayment for principal and interest be if he took out a 15-year mortgage?

1) The monthly payments if the mortgage is 30 years will be $2,270

2) The monthly payments if the mortgage is 15 years will be $3,267

Explanation:

The house is worth 500,000, John pays 100,000 down payment which means that 400,000 payment is left. We need to find out that if the present value of the payment is 400,000 then what will the monthly payments be for 30,000 in order to have a present value of 400,000.

The Present value is 400,000, the interest rate is 5.5% but because the payments are monthly we will divide it by 12 (5.5/12=0.458). The Number of compounding periods will be the number of months in 30 years so N = 30*12=360. The future value is 0 as there is no lump sum payment at the end.

We input the following information in a financial calculator in order to find the the payment.

PV = 400,000

FV=0

N=360

I=0.458

Compute PMT=2,270

Now in order to find the payments for a 15 year mortgage we will replace n=360 with n=15*12 = 180.

PV = 400,000

FV=0

N=180

I=0.458

Compute PMT=3,267