Question

You have just turned 30 years​ old, have just received your​ MBA, and have accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as​ follows: Every dollar in the plan earns 9 % per year. You cannot make withdrawals until you retire on your 60 th birthday. After that​ point, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 60. You estimate that to live comfortably in​ retirement, you will need $ 98 comma 000 per year starting at the end of the first year of retirement and ending on your one hundredth birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your​ retirement?

Answer 1

Answer:

Annual deposit= $21,568.87

Explanation:

Giving the following information:

You have just turned 30 years​ old. Every dollar in the plan earns 9 % per year. You cannot make withdrawals until you retire on your 60th birthday.

You will need $ 98,000 per year starting at the end of the first year of retirement and ending on your one-hundredth birthday.

First, we need to calculate the total amount needed at age 60.

Final value= 30years*98,000= $2,940,000

To calculate the annual deposit we need the following formula:

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

A= annual deposit

Isolating A:

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

A= (2,940,000*0.09)/[(1.09^30)-1]= $21,568.87