Mortgages

Almost everyone who buys a home requires a loan from the bank.

• A mortgage is repaid over a set length of time, known as the amortization period.

• A mortgage is a loan specifically given for the purchase of a house.

•During this period (could be up to 30 years), the conditions of the mortgage usually change (interest).

•Mortgage calculations are done using the present value of an annuity formula.

In Canada, Mortgages must be compounded S-A (says the Feds), but most

people tend to make monthly payments.

• The discrepancy between compounding periods and payments periods must be addressed before any calculations can be made.

Converting a S-A rate to a monthly rate:

• Suppose you can get a mortgage rate of 8%.

• Let the monthly interest rate be i.

• We will consider 2 ways of looking at the interest calculation.

Option #1

Consider the interest on $1.00 (C:M) for 6 months.

$1.00(1 + i)6

= (1 + i)6

Option #2

Consider the interest on $1.00

(C:S-A) for 6 months.

$1.00(1.04)1

= (1.04)1

KEY

Since these 2 options must yield the same interest

Take the 6th root of each side

(1 + i)6 = (1.04)1

[(1 + i)6]1/6 = [(1.04)1]1/6

1 + i = 1.006 558 197 i = 1.006 558 197 - 1

i = 0.656%

John gets approved for a mortgage of $100 000 at 8.5% for 25 years.

a) What are the monthly payments?

b) How much interest does John pay?

First, convert the interest:

i = 8.5% (C:S-A) = 8.5 / 2 = 0.0425

(1 + i)6 = 1.0425

i = 0.696%

n = 12 months X 25 years = 300 cycles

Use the formula for present value:

For monthly payments, use the KEY

PV = R[1 – (1 + i)-n]i

R = ?,

PV = 100 000

i = 0.00696

n = 300

100 000 = R[1 – (1 + 0.00696)-300]0.00696

R = $795.28

How much interest was paid?

b) 300 payments of $795.28

John pays 300 X $795.28 = $238 583.42

Therefore: $238 583.42 - $100000 =

$138 583.42 in interest !!!!!He pays more in interest than the entire cost of the house…