Question

Consider a typical $1,000,000 Canadian mortgage contract. Suppose that the current nominal interest rate is 6% and the maturity is set at 20 years. The rollover period is 3 years. The borrower and lender agree to a semi-annual mortgage payment scheme. Find the semi-annual annual payments on this mortgage for the first three years.

Answer 1

Mortgage = $ 1000000, Rollover Period = 3 years (implies that the principal outstanding at the end of each three year period is required to be refinanced at the then applicable interest rates)

Mortgage Tenure = 20 years or 40 semi-annual periods

Interest Rate = 6 % per annum or (6/2) = 3 % per semi-annual period

Let the semi-annual mortgage payments be $ K

Therefore, 1000000 = K x (1/0.03) x [1-{1/(1.03)^(40)}]

1000000 = K x 23.1148

K = 1000000 / 23.1148 = $ 43262.4

Semi-Annual payments for the first three years = K = $ 43262.4. Post Year 3, the outstanding mortgage balance will be refinanced at the then applicable interest rate so as to adhere to the 3 year rollover period clause.