Suppose you buy a house for $640,000 and you have $90,000 in savings which you u

Question

Suppose you buy a house for $640,000 and you have $90,000 in savings which you use as a down payment. The rest you finance with a 5-year mortgage with monthly payments and a quoted interest rate of 3.2% APR. In Canada, mortgage rates are quoted with semi-annual compounding, so this rate is an APR with semi-annual compounding and monthly payments.

(c) How much do you still owe after 3 years (i.e. immediately after you have paid the 36th payment)

(d) What is the amortization amount on the 37th mortgage payment?

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Explanation / Answer

Loan amount = 640,000 - 90,000 = 550,000

Annualized rate = (1 + 3.2%/2)^2 - 1 = 3.23%

Monthly rate = 3.23%/12 = 0.27%

Monthly payment, P = r x PV / (1 - (1 + r)^-n) = 0.27% x 550,000 / (1 - 1 / (1 + 0.27%)^60) = $9,938.02

Amount Owe after 3 years = PV x (1 + r)^n - P / r x [(1 + r)^n - 1]

= 550,000 x (1 + 0.27%)^36 - 9,938.02 / 0.27% x [(1 + 0.27%)^36 - 1]

= $230,681.72.... c)

Interest paid on 37th payment = 230,681.72 x 0.27% = $620.07

Amortization amount = 9,938.02 - 620.07 = $9,317.94.... d)

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