20.4 Reducing Balance 20.4 Reducing Balance LoansLoans

Reducing balance loansReducing 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.

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:(a)P=12,000 r=16% repayments= 27001st year:Interest = 12000 x (1 + 16/100)1 – 12000 = 1920Balance = (12000 + 1920) – 2700 = $11220

2nd year:Interest = 11220 x (1 + 16/100)1 – 11220 = 1795.20Balance = 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