A loan is repayable by a decreasing annuity payable annually in arrears for 20 years. The repayment at the end of the first year is $6,000 and subsequent repayments reduce by $200 each year. The...

Extracted text: A loan is repayable by a decreasing annuity payable annually in arrears for 20 years. The repayment at the end of the first year is $6,000 and subsequent repayments reduce by $200 each year. The repayments were calculated using an effective rate of interest of 9% per annum. (a) Calculate the original amount of the loan. (b) Immediately after the ninth payment of interest and capital, the interest rate on the outstanding loan is reduced to 7% per annum effective. Calculate the amount of the tenth payment if subsequent payments continue to be reduced by $200 each year, and the loan is to be repaid by the original date, i.e. 20 years from commencement.