Question

Consider a floating rate mortgage loan of $250,000 for amortization period of 15 years. Assume monthly mortgage payments and mortgage rate reset period every 3 months. The mortgage rate will be reset as follows: Mortgage rate the beginning-of-the-period prime rate + 3%. Mortgage rate will be compounded monthly. Suppose the prime rate today is 2.5% per annum while at the beginning of the next quarter it is expected to be 3% annum. Calculate monthly mortgage payments in the first month and the fourth month of the loan.

Answer 1

Loan = 250,000; N (in months) = 15*12 = 180; annual rate at the beginning of month 1 (M1) = 2.5%+3% = 5.50% p.a.

annual rate at the beginning of month 4 (M4) = 3% + 3% = 6.00% p.a.

PV = 250,000; N = 180; rate = 5.50%/12 = 0.46%, solve for PMT.

M1 payment = 2,042.71

This is the payment for first three months after which the rate is reset. Outstanding balance at the end of 3 months is:

rate = 0.46%; N = 180-3 = 177; PMT = 2,042.71, solve for PV. Outstanding balance = 247,297.02

PV = 247,297.02; N = 177; rate = 6%/12 = 0.5%, solve for PV. M4 payment = 2,108.69