Question

Kevin made contributions to a Roth IRA over the course of 40 working years. His contributions averaged $3,000 annually. Kevin was in the 25% tax bracket during his working years. The average annual rate of return on the acount was 7%. Upon retirement, Kevin stopped working and making Roth IRA contributions. What is the effective value of Kevin's Roth IRA at retirement?

Answer 1

A. $ 449,179.01
B. $ 568,905.34
C. $ 580,905.34
D. $ 586,905.34

Answer 2

Have you considered accumulating the sum?

Of course, it will be a very rough approximation as it is unlikely that Beginning-of-Year or End-of-Year will be useful assumptions. And that "average contribution" thing is horrible.

i = 0.07
Tax = 0.25
Accumulation Interest = i*(1-Tax) = 0.07(1-0.25) = 0.07*0.75 = 0.0525

Give it a go!

Answer 3

@tkhunny accumulation interest = 0.0525?

Answer 4

Accumulate away!

Answer 5

...sorry but what am I accumulating? @tkhunny

Answer 6

Please reread the problem statement.

Answer 7

@tkhunny I still don't follow :(

Answer 8

Why have you been given this problem?

Year 1 at the end: $3000
Year 2 at the end: $3000(1.0525) + $3000
Year 3 at the end: $3000(1.0525)^2 + $3000(1.0525) + $3000
etc.
Year 40 ---

Answer 9

@tkhunny Is there a formula to calculate the cost of all 40 years at once without listing each year?

Answer 10

Answer was B. $ 568,905.34,

Answer 11

Yes, there is. You should have seen it long before you saw this problem.