Question

Scheduled payments of ​$919​, ​$1394​, and ​$333 are due in one year​, four-and-a-half ​years, and five-and-a-half years respectively. What is the equivalent single replacement payment three years from now if interest is 9.9% compounded annually ?

The equivalent single replacement payment is ​$?

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

We need to find equivalent single replacement payment three years from now. Above pic shows timeline of years and amount due.

• For amount due in one year, we need to find future value at year 3rd. So we need to move 2 years forward

Future value = Present Value (1+ i)^n = 919 (1+9.9%)^2 =$1109.969119

• For amount due in 4.5 years, we need to find value at year 3rd. So we need to move 1.5 years back

Present value = Future Value/(1+ i)^n = 1394/(1+9.9%)^1.5 =$1209.946688

• For amount due in 5.5 years, we need to find value at year 3rd. So we need to move 2.5 years back

Present value = Future Value/(1+ i)^n = 333/(1+9.9%)^2.5 =$262.996520

equivalent single replacement payment is ​$ = $1109.969119 + $1209.946688 +  $262.996520

= $2582.912