Question

What annual sinking fund payment would be required to yield $ 4,400 5 years from​ now? The annual interest rate is​ 6% compounded semiannually. Round to the nearest cent.

Answer 1

Desired sum in 5 years = $4,400

Annual interest rate = 6.00%
Semiannual interest rate = 3.00%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.03)^2 - 1
Effective annual rate = 1.0609 - 1
Effective annual rate = 0.0609 or 6.09%

Let annual payment be $x

$x*1.0609^4 + $x*1.0609^3 + $x*1.0609^2 + $x*1.0609 + $x = $4,400
$x * (1.0609^5 - 1) / 0.0609 = $4,400
$x * 5.647231 = $4,400
$x = $779.14

So, your annual sinking fund payment will be $779.14