Simple Interest
Example 1
I purchase a car valued at $12 000 with a 30%
deposit and the balance paid off with monthly
instalments over 2 years at a rate of 8.5% p.a.
Find
(a) The amount of the deposit
(b) The balance owing
(c) The interest on this balance
(d) The total to be repaid
(e) The amount of each monthly instalment
(a) The amount of the deposit
30% of $12000
= 0.3 x 12000
= $3600
(b) The balance owing
= original amount – deposit
= 12000 - 3600
= $8400
(c) The interest on this balance
= PRT/100
= 8400 x 8.5 x 2 / 100
= $1428
(d) The total to be repaid
= principal + interest
= $8400 + 1428
= $9828
(e) The amount of each monthly instalment
= $9828 ÷ 24
= $409.50
Example 2
I want to buy a sound system valued at $12000.
I decide to pay $3000 deposit, then get a loan to
pay the remainder off over 3 years.
My monthly instalments (repayments) are $313.75.
Find
(a) The amount that I have to borrow
(b) The total that I repay in instalments
(c) The amount of interest that I pay
(d) The effective interest rate per annum, i.e. the
simple interest rate that I am paying
(a) The amount that I have to borrow
= 12000 - 3000
= $9000
(b) The total that I repay in instalments
= $313.75 x 36
= $11295
(c) The amount of interest that I pay
= Total of all instalments - principal
= $11295 - 9000
= $2295
(d) The effective interest rate per annum, i.e. the
simple interest rate that I am paying
For this we use the “R” version of the
simple interest formula, i.e.
R = 100 I / PT
I = 2295
P = 9000
T=3
R = (100 x 2295) / (9000 x 3)
R = 8.5
The annual effective interest rate is therefore 8.5% p.a.