SOLUTION: Suppose that between the ages of 22 and 32​, you contribute ​$5000 per year to a​ 401(k) and your employer contributes ​$2500 per year on your behalf. The i

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Question 1101867: Suppose that between the ages of 22 and 32​, you contribute ​$5000 per year to a​ 401(k) and your employer contributes ​$2500 per year on your behalf. The interest rate is 8.7​% compounded annually. What is the value of the​ 401(k) after 10 ​years? b. Suppose that after 10 years of working for this​ firm, you move on to a new job.​ However, you keep your accumulated retirement funds in the​ 401(k). How much money will you have in the plan when you reach age​ 65? c. What is the difference between the amount of money you will have accumulated in the​ 401(k) and the amount you contributed to the​ plan?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

32 - 22 = 10 years of payments.
65 - 32 = 33 years of investing the future value of the payments.

i used a financial calculator to get your results.

the financial calculator i used is the TI-BA-II-Plus

for the first part of your problem i did the following:

n = 10
i/y = 8.7
pv = 0
pmt = -7500
fv = 0

n is the number of years.
i/y is the interest rate percent per year.
pv is the present value of the investment.
pmt is the value of the investments made at the end of each year.
fv is the future value of the investment.

i then calculated fv and got $112,328.2732

$7,500 invested into our account at the end of each year yields a future value of $112,325,2732 at the end of the 10 year investment period.

for the second part of your problem i did the following:

n = 33
i/y = 8.7
pv = -112,325.2732
pmt = 0
fv = 0

n is the number of years.
i/y is the interest rate percent per year.
pv is the present value of the investment which is the future value of investments made for the previous 10 years.
pmt is the amount invested at the end of each year which is 0 in this case.
fv is the future value of the investment.

i then calculated fv and got $1,762,235.873

if i understand what is being asked is correct, then your solution is:

your contribution was $5,000 a year for 10 years.
that's a total contribution of $50,000.

the difference between the amount you accumulated in the 401k and the amount that you contributed is $1,762,235.873 - $50,000 = $1,712,235.873.