Question

Henry Bogut just received a signing bonus of $980,400. His plan is to invest this payment in a fund that will earn 8%, compounded annually. If Bogut plans to establish the AB Foundation once the fund grows to $2,879,621, how many years until he can establish the foundation? Instead of investing the entire $980,400, Bogut invests $322,600 today and plans to make 14 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the $2,879,621 foundation at the end of 14 years?

Answer 1

Solution:

Let It will take n years to establish the fund.

Therefore future value of $980,400 at 8% after n period = $2,879,621

$980,400 * (1+0.08)^n = $2,879,621

(1.08)^n = 2.9371899

Refer CI table,

n = 14 years

Therefore it will take 14 years to Bogut to establish the foundation.

If Bogut invest $322,600 today and make $X annual investment into the fund for 14 years:

Future value of $322,600 after 14 years

= $322,600 * (1.08^14) = $947,539

Future value of annual installment = $2,879,621 - $947,539 = $1,932,082

X * Cumulative FV factor at 8% for 14 period of ordinary annuity = $1,932,082

X * 24.21492 = $1,932,082

X = $79,789

Hence annual equal payment amount is $79,789