Shiva transferred his mortgage of $145 981 from CIBC to BMO for the remaining amortization period at 3.59% compounded semi-annually. He has agreed to pay rounded up payment of $2000 every month. How long will it take Shiva to pay-off his mortgage?

Question

Quizplus · Accepted Answer

First, we need to calculate the new monthly payment using the new interest rate and remaining amortization period:
n = number of periods = remaining amortization period in months = 25 years * 12 months/year – 5 years * 12 months/year = 240 months – 60 months = 180 months
i = interest rate per period = 3.59% / 2 = 1.795% 
P = principal = $145 981 
Using the formula for mortgage payments, we get:
$2000 = P * (i*(1+i)^n) / ((1+i)^n - 1)
Solving for P, we get:
P = $153 872.24
This means the mortgage balance was reduced from $145,981 to $153,872.24 when it was transferred to BMO.
Now we can use a mortgage calculator to find out how long it will take to pay off the mortgage with the new monthly payment of $2000 at 1.795% interest rate:
https://www.calculatorsoup.com/calculators/financial/mortgage-calculator.php 
Input:
- Loan amount: $153,872.24 
- Interest rate: 1.795% per period (semi-annually compounded) 
- Monthly payment: $2000 
- Start date: choose any date 
- Amortization period: leave blank (we want to find it out) 
Click "Calculate" and we get:
- Amortization period: 83 months 
This means it will take Shiva 83 months (or 6 years and 11 months) to pay off his mortgage.

Shiva Transferred His Mortgage of $145 981 from CIBC to BMO