Question

You are 30 years old today. You wish to retire at age 65. How much money must you deposit at the end of each year so that when you retire at age 65, you will be able to withdraw $2,500 at the end of each month until age 85?

Assume you can earn interest at the rate of 5.5% compounded daily during the entire period from age 30 to 85.

A detailed explaination would be helpful.

Answer 1

Firstly we need to find the effective annual rate

EAR = (1+APR/m)^m -1

= (1+ 0.055/365)^365 -1

= 0.056536

Next we need to compute the present value of funds at the time of retirement

Using financial calculator
Input:

N = 12*(85-65) = 20*12 = 240

PMT = -2500

I/Y = 5.6536/12

Solve for PV as 358889.74

This is now the FV required at retirement

Using financial calculator
Input:

FV = 358889.74

I/Y = 5.6536

N = 65-30 = 35

Solve for PMT as -3465.96

Annual deposit = $3465.96