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20.4 Reducing Balance Loans

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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.

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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

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Solution: (a) P=12,000 r=16% repayments= 2700 1 st year: Interest = 12000 x (1 + 16/100) 1 – 12000 = 1920 Balance = (12000 + 1920) – 2700 = $11220 2 nd year: Interest = 11220 x (1 + 16/100) 1 – 11220 = 1795.20 Balance = 11220 + 1795.20 – 2700 = 10,315.20 etc. End of YearInterestRepaymentBalance 119202,700$11,220 21795.202,700$10,315.20 31650.432,700$9265.63 41482.502,700$8048.13

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(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

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