20.4 Reducing Balance
Loans

A reducing balance loan is a loan that
attracts compound interest, but where
regular payments are also made.

In most instances, the amount of the loan
and interest are repaid in full.
Reducing balance loans
Example: A loan of $12,000 is to be repaid in instalments of
$2700 per year with an interest rate of 16% per annum
being charged on the unpaid balance at the end of each year.
After four repayments, calculate:
(a)
The amount still owing
(b)
The interest charged to date
Solution:
P=12,000 r=16% repayments= 2700
1st year:
Interest = 12000 x (1 + 16/100)1 – 12000 = 1920
Balance = (12000 + 1920) – 2700 = $11220
(a)
2nd year:
Interest = 11220 x (1 + 16/100)1 – 11220 = 1795.20
Balance = 11220 + 1795.20 – 2700 = 10,315.20 etc.
End of Year Interest
Repayment Balance
1
1920
2,700
$11,220
2
1795.20
2,700
$10,315.20
3
1650.43
2,700
$9265.63
4
1482.50
2,700
$8048.13
(b) The interest paid to date is calculated by summing the interest column.
ie. 1920 + 1795.20 + 1650.43 + 1482.50 = 6848.13
Solution: The interest charged after 4 years is $6848.13