jdlogo

jdlogo

jdlogo

jdlogo

jdlogo

Home

Simple & Compound Interest

Present Value

Ordinary Annuities

Present Value Annuities

General Annuities & Equivalent Rates

Mortgages

Review&Test

 

jdsmathnotes

 

 


 UNIT 11 : MATHEMATICS OF INVESTMENT

 LESSON 6: MORTGAGES

 

Example 1:

a) Camille has just purchased a new house near Brantford. She needs a mortgage of $150 000 after her down payment.. She will repay it in monthly instalments over 25 years.

The interest rate is 6.6%/a, compounded semi-annually. Find the monthly payment.

b) Determine the total interest paid over the 25 year period.

Solution:

Here the payment interval( monthly ) is different than the interest period ( semi-annual). This is a general annuity.

We must match the interest period to the payment interval.

Ie. We must find the monthly rate that is equivalent to 6.6%/a, compounded semi-annually.

 

Step 1: Using the formula A = P(1 + i)n, find the value of $1 invested at 6.6%/a, compounded semi-annually after 1 year.

Step 2: Let the equivalent monthly rate be i %. (Note the equivalent yearly rate would be 12i %.)

Now find the value of $1 invested at i % per month after 1 year.

A = 1(1 + i)12 ** n = 12, the number of times interest is compounded per year.

Step 3: These two amounts must be equal. Hence

 

The money in question is borrowed now at point 0 on the time line. Hence this is a PV general annuity question

 

Interest Period 0 1 2 3 298 299 300

Payment R R R R R R

R(1.005425865)-1

R(1.005425865)-2

.

.

R(1.005425865)-298

R(1.005425865)-299

 

R(1.005425865)-300

 

 

This forms the following geometric series:

R(1.005425865)-300 + R(1.005425865)-59 + . . . + R(1.005425865)-2 + R(1.005425865)-1

 

 

b) Determine the total interest paid over the 25 year period.

 

Total amount repaid = 1013.85 x 300 = $304 095.00

Mortgage amount = $150 000

 

Interest paid = $304 095 - $!50 000 =$154 095

Hence the total interest paid over 25 years is $154 095.

 

Return to top of page

Click here to go to homework questions