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Amy​ Parker, a​ 22-year-old and newly hired marine​ biologist, is quick to admit that she does not plan to keep close tabs on how her​ 401(k) retirement plan will grow with time. This sort of thing does not really interest her.​ Amy's contribution, plus that of her​ employer, amounts to ​$2 comma 150 per year starting at age 23. Amy expects this amount to increase by 3​% each year until she retires at the age of 57 ​(there will be 35 EOY​ payments). What is the compounded future value of​ Amy's 401(k) plan if it earns 5​% per​ year?

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Answer:

Final Value= $370,481.13

Explanation:

Giving the following information:

Amy's contribution, plus that of her​ employer, amounts to ​$2,150 per year starting at age 23. Amy expects this amount to increase by 3​% each year until she retires at the age of 57 ​(there will be 35 EOY​ payments). Interest rate= 5%.

First, we will add the growth of the deposits to the interest rate:

Interest rate= 0.03 + 0.05= 0.08

Now, to calculate the final value, we need to use the following formula:

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

A= annual deposit= 2,150

i= 0.08

n= 35

FV= {2,150*[(1.08^35)-1]}/ 0.08= $370,481.13

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