Question

Lauren will make annual contributions in the amount of $4,770, on average, to a 401(k) over the next 34 years. Her employer will match 60% of her contributions. She is currently being taxed at 33%, but anticipates being taxed at 15% upon retirement. If her account grows at an average rate of 5.5% annually, what is the value of Lauren's 401(k) upon retirement?

$381,435.69

$395,228.47

$481,057.72

$610,297.11

And please explain why!!!!

Answer 1

$610,297.11

Explanation:

The problem seems to make several assumptions:

• contributions are made at the end of each year
• contributions and employer matching funds are not taxed until retirement
• the 15% tax rate applies to the account balance amount at retirement

Of these, the last is least likely to be true in the United States.

___

Based on the assumptions above, we compute the amount from the future value of the series of contributions, then subtract 15% from that result.

FV = P·((1 +r)^n -1)/r . . . . where P is the amount of each payment, r is the annual interest rate, n is the number of payments.

The amount deposited each year is ...

$4770 + 0.60·4770 = $7630

Then the future value after 34 deposits is ...

FV = 7630·(1.055^34 -1)/0.055 ≈ 717,996.60

When this amount is reduced by the assumed 15% tax rate, it becomes ...

$717,996.60 - 0.15·717,996.60 = $610,297.11