Question

You have just turned 22 years old, and have accepted your first job. Now you will decide how much money to put into your retirement plan. The plan works as follows: You expect to live to 100 and work until you turn 65. You estimate that you will need $100,000 per year, starting at the end of the first year of your retirement (i.e. when you turn 66) and ending on your one-hundredth birthday. You will contribute the same amount to the retirement plan at the end of every year when you work (i.e., from your age of 23 to your age of 65). Every dollar in the plan earns 7% per year. How much do you need to contribute each year to fund your retirement?

Answer 1

Answer:

Annual deposit= $71,428.57 per year

Explanation:

Giving the following information:

You expect to live to 100 and work until you turn 65. You estimate that you will need $100,000 per year.

Every dollar in the plan earns 7% per year.

You have just turned 22 years old.

First, we need to calculate the amount of money necessary in retirement:

Final value= 100,000*35 years= 3,500,000

Now, using the following formula, we calculate the yearly deposit needed:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

n= 65-22= 43

FV= 3,500,000

i=0.07

A= (3,500,000*0.07)/[(1.07^22)-1]

A= 245,000/3.43

A= 71,428.57 per year