Question

Herman has agreed to repay a debt by using the following repayment schedule. Starting today, he will make $100 payments at the beginning of each month for the next two-and-a-half years. He will then pay nothing for the next two years. Finally, after four-and-a-half years, he will make $200 payments at the beginning of each month for one year, which will pay off his debt completely. For the first four-and-a-half years, the interest on the debt is 9% compounded monthly. For the final year, the interest is lowered to 8.5% compounded monthly. Find the size of Herman’s debt. Round your answer to the nearest dollar.

Answer 1

Loan value is PV of all the future cash flows

PV of $100 for 2.5 yrs $2,697.59 =-PV(9%/12,30,100,,1)

PV of $200 for last yrs $1,542.58 =-PV(8.5%/12,12,200,,1)/(1+9%/12)^54

Loan value $4,240.17

Rounding off = $4240.