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.

a) 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

a. 6 month rate = 1.0321/2 - 1 = 1.5874%

Effective rate = (1 + 1.5874%/6)^12 - 1 = 3..2214%

Effectuve rate of car loan = (1 + 3.2%/12)^12 - 1 = 3.2474%

the effective rate of car loan is more than the mortgage

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