SOLUTION: Suppose that between the ages of 23 and 45, you contribute $4000 per year to a 401(k) and your employer contributes $2000 per year on your behalf. The interest rate is 8.3% compoun

Question 1198382: Suppose that between the ages of 23 and 45, you contribute $4000 per year to a 401(k) and your employer contributes $2000 per year on your behalf. The interest rate is 8.3% compounded annually. (a) What is the value of the 401(k), rounded to the nearest dollar, after 22 years?
(b) Suppose that after 22 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, to the nearest dollar, 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?
Group of answer choices

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the annual growth rate is 1.083.
you are contributing 4000 at the end of each year and your company i contributing 2000 at the end of each year for a total of 6000 at the end of each year.
after 22 years, the value in your account will be equal to 345,444.2462.
you will be 45 years of age.
you invest that at the same rate of interest for an additional 20 years until you are 65.
the value at that time will be equal to that * 1.083 ^ 20 = 1,701,951.171.
round to 2 decimal places to get 1,701.951.17.

here are what the yearly transactions look like.

you contributed 4000 at the end of each year for a total of 4000 * 22 = 88,000
the value of the 401k at the end of 42 years = 1,701,951.17.
the difference is equal to 1,613,951.17.

42 years is 22 years of investment in the 401k until you are 45 years old and then another 20 years until you are 65 years old.

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