Question

You have just negotiated a 5-year mortgage on $400,000 amortized over 25 years at a rate of 3.5%. After 5 years assume that the mortgage rate remains the same, but you increase the payments by 500 dollars per month, in how many periods (months) will you be able to pay the whole amount. (Hint: Canadian banks quote mortgage rates as a rate per year compounded semi-annually)

Answer 1

Effective monthly rate, r = (1 + 0.035/2)^(1/6) - 1

r = 0.002895623966

n = 25 * 12 = 300

PV = 400,000

This is the original payment

Now, we will find the loan outstanding at the end of 5 years

n = (25 - 20) * 12 = 240

PMT = 1,997.0813293829

r = 0.002895623966

Next, we will find the number of months required to payoff this loan outstanding with PMT = 1,997.0813293829 + 500

PMT = 2497.0813293829

PV = -345119.927872556

FV = 0

I/Y = 0.2895623966

CPT N

N = 176.7848517

N ~ 177 months

The number of months required to payoff the whole amount = 60 + 177

The number of months required to payoff the whole amount = 237 months