Question

Al Darby wants to withdraw $21300 (including principal) from an investment fund at the end of each year for five years. How should he compute his required initial investment at the beginning of the first year if the fund earns 11% compounded annually?

Answer 1

PV= $78,722.61

Step-by-step explanation:

Giving the following information:

Annual pay= $21,300

Interest rate= 11%

Number of periods= 5 years

First, we need to calculate the future value of the payments:

FV= {A*[(1+i)^n-1]}/i

A= annual pay

FV= {21,300*[(1.11^5) - 1]} / 0.11

FV= $132,652.17

Now, the initial deposit:

PV= FV/(1+i)^n

PV= 132,652.17/1.11^5

PV= $78,722.61

Prove:

Annual withdraw= (PV*i) / [1 - (1+i)^(-n)]

Annual withdraw= (78,722.61*0.11) / [1 - (1.11^-5)

Annual withdraw= $21,300