20.4 Reducing Balance Loans

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.

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= st year: Interest = x (1 + 16/100) 1 – = 1920 Balance = ( ) – 2700 = $ nd year: Interest = x (1 + 16/100) 1 – = Balance = – 2700 = 10, etc. End of YearInterestRepaymentBalance ,700$11, ,700$10, ,700$ ,700$

(b) The interest paid to date is calculated by summing the interest column. ie = Solution: The interest charged after 4 years is $