Question

Heeelp! Multiple choice for algebra with finances

Answer 1

Lauren will make annual contributions in the amount of $4,255, on average, to a 401(k) over the next 39 years. Her employer will match 80% of her contributions. She is currently being taxed at 28%, but anticipates being taxed at 10% upon retirement. If her account grows at an average rate of 4.2% annually, what is the value of Lauren’s 401(k) upon retirement?

A) $652,472.84
B) $641,333.54
C) $485,729.78
D) $362,484.91

I have absolutely no idea how to do this, any help is appreciated!!

Answer 2

Yuck! This is a nasty looking one... I'm trying to work it out... I'll let you know. :)

Answer 3

Thank you so much ^-^

Answer 4

still working... think I might have found a formula... were you given any formula for compound interest or anything?

Answer 5

I know the basic one, but I have no idea what formula I should use for this >_<

Answer 6

OK, just wondering... :)

Answer 7

Getting closer... :)

Answer 8

I think it is going to be A... double checking.

Answer 9

I think that should be the right answer. Here's the formula I found:

\[A(Y) = \frac{(1+r)^Y-1}{r} \cdot (\text{contribution})\]

Answer 10

We can easily find that Y = 39 years, and r = 0.042 from the given information. But finding contribution is a little more difficult (but not too bad).

Answer 11

Lauren contributes $4,255. But her employer also gives her an extra 80%. That means she gets an additional 0.80(4255) = $3404 dollars in her contribution. Total contribution = $7659.

Answer 12

Plugging this into the formula gives
\[\frac{(1+0.042)^{39} - 1}{0.042} \cdot (\$7659) = \$724,969.82\]

Answer 13

However, the question also says she will be taxed by 10% on this amount. Thus, the amount she pays in taxes is 0.10(724,969.82) = $72,496.98

Answer 14

Her final value then, is $724,969.82 - $72,496.98 = $652,472.84.

Answer 15

Yikes! A lot of steps... but certainly not impossible. Does that make sense? Any questions? :)

Answer 16

That helps soooo much! I pretty much got the whole lesson down but while I'm taking this assignment this question popped up and I had no idea how to do it :c you explained it so well, I cannot thank you enough <3 <3 <3

Answer 17

Glad to help! Good luck!

Answer 18

Just wanted to say I submitted my assignment and it indeed was the correct answer :)