Strange Final Question

[LondonBroil]

Took the final about 15 minutes ago. Maybe I'm missing something, so I copied down the problem word for word.

#14
Clark and Colby Chambers are twin-brothers and are salaried employees saving for their retirement in 2027. Both men are in the 28% marginal tax bracket.

Clark makes $1,000 annual contribution on 12/31 into a savings account earning an effective interest rate of 8% per year. At the same time, Colby makes $1,000 annual payment to an insurance company for an after-tax-deferred annuity. The annuity also earns an effective rate of 8% per year.

Assume that the men remain in the same tax bracket throughout the 20 years and disregard state income taxes.

a) Calculate how much each man will have in his investment account at the end of 20 years.

b) Compute the interest earned on each.


The wording makes it seem that each man would have a different amount, but I answered that the accounts would have the same amount ($45,761.96), but Colby would have to pay taxes on any withdrawals whereas Clark would have paid taxes each year on his earnings.

Am I right?

[LondonBroil]

Bump for the math whizzes?

[Magic_Man]

Try the finance forum? Seems like there is more than just math knowledge involved here...

[RocketManJames]

I might be misunderstanding the problem, but I don't see how the accounts could result in the same amount after many years. Tax-deferral is powerful.

Like, for example, say we both put in 10K. And, to make things simpler say that tax is 50%, and annual return is 100%. You pay tax on the profit each year, and I pay taxes at the end on the profit. Say the end of this is after 3 years.

Year 0: 10k vs 10k
Year 1: (20k - 5k) = 15k vs 20k
Year 2: (30k - 7.5k) = 22.5k vs 40k
Year 3: (45k - 11.25k) = 33.75k vs (80k - 35k) = 45k

So after 3 years, the tax-deferred account is better off than the one that pays taxes annually.

-RMJ

Edited to correct an error... and to mention that I may be totally misunderstanding how annuity payouts work in relation to taxes, etc.