You have just turned 22 years old, received your bachelor's degree, and 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 6.6 % per year. you cannot make withdrawals until you retire on your 65th birthday. after that, you can make withdrawals as you see fit. you decide that you will plan to live to 100 and work until you turn 65. you estimate that to live comfortably in retirement, you will need $ 115 comma 000 per year, starting at the end of the first year of retirement and ending on your 100th 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? your annual contribution should be $ nothing.

Your annual contribution=$87,809.24

Explanation:

Step 1: Determine total amount needed in retirement

Total amount=Expenditure per year×number of years after retirement

where;

Expenditure per year=$ 115,000

Number of years after retirement=(100-65)=35 years

replacing;

Total amount=(115,000×35)=$4,025,000

You need a total amount of $4,025,00 for your plan

Step 2: Determine contribution per year

The contribution per year is the same as principal amount per year

Total amount needed per year=4,025,000/(65-22)=93,604.65 per year

Using the formula

A=P(1+r)^n

where;

A=Future value per year=$93,604.65

P=unknown=p

r=6.6%=6.6/100=0.066

n=1

replacing;

93,604.65=p(1+0.066)^1

93,604.65=1.066 p

p=93,604.65/1.066

p=87,809.24

Your annual contribution=$87,809.24

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