Question

Marie, an employee at McCormick, has determined that she will need $5000 per month in retirement over a 30-year period. She has forecasted that her money will earn 7.2% compounded monthly. Marie will spend 25-years working toward this goal investing monthly at an annual rate of 7.2%. How much should Marie’s monthly payments be during her working years in order to satisfy her retirement needs?  Hint: Find how much Marie must have at retirement, then find the monthly payments to reach that goal.

What maximum amount could Marie withdraw each month so that her balance never decreases (nearest dollar)?

Answer 1

First, we find the present value of Marie's retirement per month amount at the start of retirement.

Using a financial calculator

FV = 0

PMT = 5000

N = 360 (30 years*12 payments per year = 360periods)

I/Y = 7.2/12

cpt PV, we get PV = 736606.78

This amount is the future value of the monthly payments. We now estimate the monthly payment required for this amount

Using a financial calculator

PV = 0

FV = 36606.78

PMT = 5000

N = 300 (25 years*12 payments per year = 300 periods)

I/Y = 7.2/12

cpt PMT , we get PMT  = 880.90

Hence, Marie needs to make monthly payments of $880.90 for 25 years to reach retirement goals.

The maximum Marie can withdraw on a monthly basis after retirment which doesn't reduce her balance is equal to the monthly interest on the $736606.78

Hence, 7.2*736606.78/(12*100) = $4420, she can withdraw without reducing her balance.