Question

When you reach retirement​ age, you would like to have enough money saved to be able to​ “pay yourself” an annual salary of

​$76

​,000

per year for 20 years. To put this another​ way, your plan is to start your retirement with a large amount of money​ saved, and you will withdraw

​$76

​,000

from these savings once a year for the next 20 years until all of your savings are depleted.

In the​ meantime, you are a​ 25-year-old new UIC​ graduate, and you plan on working for 40 years until you retire. To fund your retirement​ goals, you plan on investing some money in the stock market. More​ specifically, at the end of each year until you​ retire, you are going to put part of your paycheck into the stock​ market; you'll put in the same dollar amount every year for the next 40 years.

You are a pretty decent stock​ investor, and you think you can make a

14

​%

return on the market each year you​ invest, both until you retire and after retirement.

What is the annuity payment​ (to the nearest​ dollar) you need to put into the stock market every year for the next 40 years to fully fund your​ retirement?

Write your​ answer, without a dollar sign in​ front, rounded to the nearest whole dollar. ​ (If you do this​ correctly, it might be a smaller number than​ you'd think!)

Answer 1

First, we calculate the amount required at retirement to enable the yearly withdrawals during retirement. The amount required at retirement is calculated using PV function in Excel :

rate = 14% (rate of return earned)

nper = 20 (number of years in retirement)

pmt = -76000 (yearly withdrawal. This is entered with a negative sign because it is a withdrawal)

PV is calculated to be $503,357.92

Next, we calculate the yearly saving required to accumulate the required amount at retirement. The yearly saving required is calculated using PMT function in Excel :

rate = 14% (rate of return earned)

nper = 40 (number of years until retirement)

pv = 0 (amount currently saved is zero)

fv = 503357.92 (required amount at retirement)

PMT is calculated to be $375.07

The annuity payment​ (to the nearest​ dollar) is $375