Everything Maths Grade 12

4.3 CHAPTER 4. FINANCE

Example 2: Monthly mortgage repayments

QUESTION

Sam is looking to buy his first flat, and has R15 000 in cash savings whichhe will use as a

deposit. He has vieweda flat which is on the market for R250 000, and he would like to work

out how much the monthly repayments wouldbe. He will be taking out a 30 year mortgage

with monthly repayments. The annual interest rate is 11%.

SOLUTION

Step 1 : Determine what is given and what is needed

The following is given:

• Deposit amount = R15 000


• Price of flat = R250 000


• interest rate, i = 11%
  We are required to findthe monthly repaymentfor a 30-year mortgage.

Step 2 : Determine how to approach the problem

We know that:

X =

M

[(1−(1+i)

−n)

i ]

In order to use this equation, we need to calculateM , the amount of the mortgage

bond, which is the purchase price of property less the deposit which Sam pays

upfront.

M = R250 000− R15 000

= R235 000

Now because we are considering monthly repayments, but we have been

given an annual interestrate, we need to convert this to a monthly interest rate,

i 12. (If you are not clear onthis, go back and reviseSection ??.)

(1 +i 12 )^12 = (1 +i)

(1 +i 12 )^12 = 1, 11

i 12 = 0,873459%

We know that the mortgage bond is for 30 years, which equates to 3 60

months.

Step 3 : Solve the problem

Now it is easy, we canjust plug the numbers in the formula, but do not forget

that you can always deduce the formula from first principles as well!

X =

M

[(1−(1+i)

−n)

i ]

=

R235 000

[(1−(1.00876459)

− (^360) )
0 , 008734594 ]
= R2 146, 39
Step 4 : Write the final answer