Question

When you reach retirement​ age, you would like to have enough money saved to be able to​ “pay yourself” an annual salary of ​$74​,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 ​$74​,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 20​%

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

Annual payment at retirement = $74,000

Years in Retirement = 20

Nominal return on investments, r = 20% per year

Amount needed at retirement can be calculated using PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = annual return = 20%

number of periods = years in retirement = 20

payment amount = Annual payment at retirement = $74,000

future value = 0

when-due = when is the withdrawal made each year = beginning = 1

Amount needed at retirement = PV(20%, 25, 74000, 0, 1) = $439,345.73 --------------(1)

Years to retirement = 40

If you invest $1 each year, the future value of these investments after 40 years can be calculated using the FV function in spreadsheet

FV(rate, number of periods, payment amount, present value, when-due)

Where, rate = annual return = 20%

number of periods = years to retirement = 40

payment amount = yearly investment = $1

present value = present value of investments = 0

when-due = when is the investment made each year = end = 0

Future value of $1 investments at retirement = FV(20%, 40, 1, 0, 0) = $7,343.86

This is the value of $1 invested every year for 40 years, at retirement. If instead of $1, amount A is invested

Future Value of A invested for 40 years, at retirement = 7,343.86A -----------------(2)

Equating (1) and (2)

7,343.86A =  439,345.73

A =  439,345.73/7,343.86 = $59.82

You would need to invest $59.82 at the end of each year for 40 years, to cover for your retirement needs