Question

What is the annual equal amount of money you have to set aside to guarantee yourself an annual income to perpetuity of $65,000 starting in 41 years from now? You make the first payment in two years from now and the last payment in 40 years. Assume an interest rate of 4% (EAR).

Answer 1

Step 1:
The first step is to find out the amount that should be available at the beginning of the 40th year to be able to pay a perpetuity of $65000 = 65000/0.04 =	$     1,625,000
Step 2:
The second step is to find the amount to be paid from t2 to t40, a total of 39 instalments whose FV should be $1625000.
So 1625000=A*FVIFA(4,39)
where A=the yearly amount to be deposited.
Solving for A
1625000 = A*90.4091
A = 1625000/90.4091 = $17,973,.85