Question

A borrower took out a loan of 100,000 and promised to repay it with a payment at the end of each year for 30 years.

The amount of each of the first ten payments equals the amount of interest due. The amount of each of the next ten payments equals 150% of the amount of interest due. The amount of each of the last ten payments is X.

The lender charges interest at an annual effective rate of 10%.

Calculate X.

Answer 1

Initially the outstanding balance is 100000. The interest on this will be 10%, that is 10000. Hence, for the first 10 years, the instalment paid will be 10,000 each year and there will be no reduction in the outstanding balance as only interest is paid.

From 11th year onwards, the amount paid will be 150% of the interest due. For 11th year, interest due will be 10,000 but amount paid is 15,000. Thus, the extra 5000 paid, will be adjusted towards the principle which will reduce to 95,000.
Hence, for 12th year, the interest will be 9500, while the amount paid is 150%, which is 14,250, thus the extra amount is adjusted in principal. This will continue till year 20 as shown in excel.

From year 21 onwards, the equal amount will be paid, which is calculated using PMT function in excel.

The rate will be 10%,
PV will be the outstanding balance after the 20th payment,
nper will be number of remaining payment that is 10

PMT found is 9744.17, which is the answer X