Question

How much must I invest today if I want to withdraw 1/3 of my original investment in 3 years, 1/3 in 4 years, and $25000 in 5 years? the investment will earn interest at 8% compounded quarterly.

The correct answer is $14378.47, but I don't know how to calculate it, please help me solve it, thank you.

Answer 1

Let amount invested today be $x

Annual interest rate = 8.00%
Quarterly interest rate = 2.00%

Amount withdrawn in 3 years or 12 quarters = (1/3)*$x
Amount withdrawn in 4 years or 16 quarters = (1/3)*$x
Amount withdrawn in 5 years or 20 quarters = $25,000

$x = (1/3)*$x/1.02^12 + (1/3)*$x/1.02^16 + $25,000/1.02^20
$x = $x * 0.262831 + $x * 0.242815 + $16,824.28
$x * 0.494354 = $16,824.28
$x = $34,032.86