Question

Joe wants to get a buy a condo, and the following information is available to him:

Purchase price: 600,000 CAD

20% Down payment: 120,000 CAD

Interest rate: 3.5% compounded semi-annually (25-year mortgage, i.e. 300 months)

a) What is the monthly mortgage payment Joe needs to make?

b) How much total interest would Joe have paid over the life of the mortgage (25

years, 300 months), assuming the same interest rate over the life of mortgage.

c) If Joe sells the place after 3 years, what would be the balance of the mortgage at

the end of year 3 that Victor owes to the bank?

Answer 1

a). Loan Amount = Purchase Price - Down payment

= 600,000 CAD - 120,000 CAD = 480,000 CAD

First convert the semi-annually compounded rate to EAR;

EAR = [1 + (APR/m)]^m - 1; m = no. of compounded periods in a year;

= [1 + (0.035/2)]² - 1

= [1.0175]² - 1

= 1.0353 - 1 = 0.0353, or 3.53%

Now, convert EAR to APR monthly compounded;

APR = m * [(1 + EAR)^1/m - 1]

= 12 * [(1 + 0.0353)^1/12 - 1]

= 12 * [1.0029 - 1] = 12 * 0.0029 = 0.0347, or 3.47%

Monthly payment = [Loan Amount * r] / [1 - (1 + r)^-n]

= [480,000 * (0.0347/12)] / [1 - {1 + (0.0347/12)}^-300]

= 1,389.90 / 0.5800 = 2,396.50 CAD

b). Total Amount Paid = Monthly Payment * No. of Payments

= 2,396.50 * 300 = 718,949.27 CAD

Interest Paid= Total Amount Paid - Mortgage Amount

= 718,949.27 - 480,000 = 238,949.27 CAD

c). Loan Balance after t payments = [Loan Amount * {(1 + r)^n - (1 + r)^t}] / [(1 + r)^n - 1]

Loan Balance after 36 payments = [480,000 * {(1 + 0.0347/12)^300 - (1 + 0.0347/12)^36}] / [(1 + 0.0347/12)^300 - 1]
= [480,000 * {2.3808 - 1.1097}] / [2.3808 - 1]

= [480,000 * 1.2711] / 1.3808

= 610,121.57 / 1.3808 = 441,864.46 CAD