Question

Suppose that between the ages of 22 and

36​,

you contribute

​$9000

per year to a​ 401(k) and your employer contributes

​$4500

per year on your behalf. The interest rate is

7.9​%

compounded annually. What is the value of the​ 401(k) after

14

​years? b. Suppose that after

14

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?

a. The value of the​ 401(k) after

14

years is

​$nothing.

​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

b. The money accumulated in the plan when reaching age 65 is

​$nothing.

​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

c. The difference between the amount of money you will have accumulated in the​ 401(k) and the amount you contributed to the plan is

​$nothing.

​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

Answer 1

a]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $13,500

r = periodic rate of interest. This is 7.9%

n = number of periods. This is 14

value of the​ 401(k) after 14 years = $13,500 * [(1 + 7.9%)¹⁴ - 1] / 7.9%

value of the​ 401(k) after 14 years = $324,572

b]

future value of lumpsum = present value * (1 + rate)^{number of years}

money accumulated in the plan when reaching age 65 =  $324,572 * (1 + 7.9%)²⁹

money accumulated in the plan when reaching age 65 =  $2,943,967

c]

Difference = money in plan at age 65 - total amount contributed

Difference = $2,943,967 - ($13,500 * 14)

Difference = $2,754,967