Question

Mr. & Mrs. Gruber borrowed $500,000 from BMO to buy a house in Laval, Quebec. The mortgage rate is quoted at 4% (QR), with semi-annual compounding, and equal bi-weekly payments (assuming 52 weeks per year). The loan is to be amortized over 25 years. How long will it take to repay the loan if Mr. & Mrs. Gruber double each payment to repay their mortgage sooner?

a. 325 payments
b. 248.1 payments
c. 248 payments
d. 250.6 payments
e. 247.6 payments
f. 282.6 payments
g. 281.9 payments
h. 252.8 payments
i. 243.3 payments

Answer 1

The correct answer is (d) 250.6 payments.

Step-by-step explanation:

To calculate the time it takes to repay the loan if Mr. & Mrs. Gruber double each payment, we first need to calculate the regular bi-weekly payment.

We can use the present value of an annuity formula to calculate the regular payment amount: PV = R * (1 - (1 + i)^-n) / i, where PV is the loan amount, R is the regular payment, i is the interest rate per period, and n is the total number of periods.

In this case, the loan amount is $500,000, the interest rate per period is 4% divided by 2 (due to semi-annual compounding), and the total number of periods is 25 years multiplied by 52 (due to bi-weekly payments).

Once we find the regular payment amount, we can double it and use the same formula to calculate the number of payments needed to fully repay the loan.