Question

You buy a house for $500,000 with 5% down and amortize over 30 years.

i. Including CMHC insurance, how much will your outstanding mortgage be when the mortgage is issued?

ii. If house prices drop by 20% over 3 years and the interest rate on the mortgage is 3.59%, how much larger is the outstanding mortgage than the value of the house? (This situation is often called ‘underwater’ and can lead to a number of problems – e.g. one needs to add money to sell).

Answer 1

Purchase Price ==> 500,000

Down Payment ==> 25,000

Amortisation period ==> 30 years.

Answer A:

CMHC insurance ==> (500,000 - 25,000)*3.10%

==> $14,725

outstanding mortgage ==> 500,000 - 25,000 + 14725 ==> $539,725.

Answer B:

the rate term is over 3 years and the interest rate on the mortgage is 3.59% than outstanding mortgage at the end of the term

i ==> 3.59%/12

i ==> 0.299% ==> 0.002991

n ==> 12*30 ==> 360

Monthly Loan Payment amount

P ==>  0.002991 * 539,725 / [1-(1.002991^-360)]

P ==> $2451.01

Loan balance after n payments have been made

where n = 12* 3 ==> 36

Loan Balance

==> 539,725(1.002991)^36 -  2451.01/0.002991[(1.002991^36)-1]

==> 507,972.676

Then

Price of the house for 3 years ==>500,000 * (1-0.20)

==>$400,000

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