Question

For the Following Questions, show all work
Use equations not computer

a) 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 an annual mortgage payment scheme. Find (i) the annual payments on this mortgage for the first three years and (ii) the amounts for the principal and interest components of each of these three annual payments.

b) 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

(a) Mortgage = $ 1000000, Tenue = 20 years and Interest Rate = 6 %
Let the annual repayments be $ P

Therefore, 1000000 = P x (1/0.06) x [1-{1/(1.06)^(20)}]

1000000 = P x 11.4699

P = 1000000 / 11.4699 = $ 87184.56

(b)

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.