SOLUTION: Suppose that Ramos contributes $4000/year into a traditional IRA earning interest at the rate of 4%/year compounded annually, every year after age 37 until his retirement at age 67

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Question 1113148: Suppose that Ramos contributes $4000/year into a traditional IRA earning interest at the rate of 4%/year compounded annually, every year after age 37 until his retirement at age 67. At the same time, his wife Vanessa deposits $2800/year (the amount after paying taxes at the rate of 30%) into a Roth IRA earning interest at the same rate as that of Ramos. Suppose that Ramos withdraws his investment upon retirement at age 67 and that his investment is then taxed at 30%. (Round your answers to the nearest cent.)
How much will Ramos's investment be worth (after taxes) at that time?
How much will Vanessa's investment be worth at that time?
Answer by Theo(13342) About Me  (Show Source):
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looks like they'll both have the same amount of money at the end of the 30 year period.

for ramos:

4000 invested at the end of each year for 30 years at 4% interest rate compounded annually gives him 224,339.751 at the end of the 30 year period.

he is then taxed at 30% which nets him 157,037.8257 after taxes.

for vanessa:

2800 invested at the end of each year for 30 years at 4% interest rate compounded annually give her 157,037.8257 at the end of the 30 year period.

since her tax rate on this is 0%, she nets the whole amount of 157,037.8257.

they both wind up with the same amount of money.

given this specific scenario, it looks like there is no advantage to a roth ira, but there actually is, depending on the circumstances.

one circumstance would be if your projected tax rate in the future is greater than your tax rate now.

by using a roth ira, your money is taxed at the lower rate now and you don't have to pay any additional taxes when you retire and your tax rate is a higher rate.

also, there are different rules for roth ira than for traditional iras that may make the roth ira a better deal.

here's a reference i looked up that discusses some of those.

https://www.rothira.com/what-is-a-roth-ira

note that her investment at 2800 is 70% of 4000, which means she paid 30% tax on the 4000 up front, rather than at the end.