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. 2. (a) What is the monthly effective interest rate? Answer with sufficient decimal places. (b) How much is the monthly payment? (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? (e) Suppose your bank offers you a 3.2% APR loan for a car with monthly payments. How does the effective annual rate of this loan compare with that of the mortgage?

Explanation / Answer

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

Effective Annualized Rate (EAR) = (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)

Effective Annualized Rate (EAR) = (1 + APR/n)^n - 1 = (1 + 3.2%/12)^12 - 1 = 3.25%

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