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

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