Question

A loan of $10,000 is being repaid with 10 payments at the end of each year, where each payment includes equal amount of repayment of the principal and the interest at a rate of 5% based on the outstanding balance after the previous payment. Immediately after the loan was made, the right of the loan was sold at a price that yields an annual effective rate of 10%. Find the price paid for the right of the loan. (Answer: $8072.28) Show work and equations.

Answer 1

Repayment of the principal is made in equal yearly instalments. Hence each instalment will be of $1,000. Interest will be calculated on the principal left at the end of previous year. Thus total repayment at the end of the year will be interest paid for that year and principal repayment for that year. Price paid for the right of the loan is the sum of present value of the total repayment for the years at a discount rate of 10%. This can be calculated as workings in the table below: End result will be as follows: Hence the answer is $8,072.28