Question

A person owes $1225 at the end of 1 year(s) and $4350 at the end of 6 years. Due to financial difficulty, the person is allowed by the lender to settle both debts with a single payment at the end of 4 years using 19.5% compounded monthly for the settlement. Determine the amount required to settle both debts at the end of 4 years.

Answer 1

Future Value of payment 1 at the end of year 4

= 1,225 (1+0.195/12)^3×12

= 1,225 (1+0.0163)^36

= 1,225 (1.0163)^36

= 1,225 (1.7866)

= $2,188.59

Present Value of year 6 payment at the end of year 4

= 4,350 /(1+0.195/12)^2×12

= 4,350 / (1+0.0163)^24

= 4,350 / (1.0163)^24

= 4,350 / 1.4741

= 2,950.95

Total single payment to be made at the end of year 4 = future value of year 1 payment + Present value of year 6 payment

= 2,188.59 + 2,950.95

= $5,139.54

There might be difference in answer due to rounding off.