Question

Dan, and Mike are brothers. They plan to begin savings plans when each is exactly 25. Each brother plans to save $6,000 per year by investing $500 each month into Tax Sheltered or Tax Deferred IRAs.
Dan plans to invest his money into a stock mutual fund with a Traditional IRA earning a 9% average annual return.

Mike plans to invest into a Stock mutual fund with a Roth IRA earning a 9% average annual return.

Assume that the combined federal and state marginal income tax rate for each brother is currently 25% and will remain this percentage during their working years.

The $6,000 available for investment by each bother is before income taxes.

Also, assume that the marginal combined federal and state income taxes will be 20% for each brother during his retirement years.

Remember that the $6,000 available for investment per year is before the payment of income taxes and both will have available for investing monthly ($6,000 / 12 = $500 per month).

1. How much will Dan have in his traditional IRA account at 67? Follow the proper taxation for this type of retirement account.

A) Amount available to invest after taxes per month?

B) Amount in account at age 67?

C) Briefly explain the taxation on withdrawals from a Traditional IRA

2. How much will Mike have in his Roth IRA at age 67? Follow the proper taxation for this type of retirement account.

A) Amount available to invest after taxes per month?

B) Amount in account at age 67

c) Briefly explain the taxation on the withdrawals from a Roth IRA

3. If both brothers are expected to be taxed at a 20% tax rate in retirement, which retirement plan will have the best after tax results?

Answer 1

Answer:

1. How much will Dan have in his traditional IRA account at 67? Follow the proper taxation for this type of retirement account.

A) Amount available to invest after taxes per month?

• $500

B) Amount in account at age 67?

• $2,813,492

C) Briefly explain the taxation on withdrawals from a Traditional IRA

•  IRA contributions are made before income taxes are paid, that is why Dan's monthly contributions are higher. The disadvantage is that Dan's plan will be taxed later.

2. How much will Mike have in his Roth IRA at age 67? Follow the proper taxation for this type of retirement account.

A) Amount available to invest after taxes per month?

• $375 until 59.5 years old, then $500

B) Amount in account at age 67

• $2,072,879

c) Briefly explain the taxation on the withdrawals from a Roth IRA

• Roth IRA contributions are made after income taxes are paid, that is why Mike's monthly contributions are lower. The advantage is that Mike's plan will not be taxed later.

3. If both brothers are expected to be taxed at a 20% tax rate in retirement, which retirement plan will have the best after tax results?

• In this case, since the tax rate is higher while they are working (25%), than once they retire (20%), the traditional IRA account could make more sense except that since the time span is very long, your account will accumulate a lot of earned interest. The total principal invested into the traditional IRA account is $252,000 and the interest gained is $2,561,492 and that part will be taxed once you start withdrawing money. In order to determine which account would be better, you need to estimate how many years will Dan and Mike live after retiring, the longer they live the best option is the Roth IRA account.  

Explanation:

the formula to determine the future value of an annuity is:

FV = P x [(1 + r)ⁿ - 1] / r

Dan's monthly contribution = $500

Mike's monthly contribution = $500 x (1 - 25%) = $375 until age 59.5, then $500

Dan's n =  42 years x 12 months = 504

r = 9% / 12 = 0.75%

Mike's n = 414 for $375 and 90 for $500

Dan's FV = $500 x [(1 + 0.75%)⁵⁰⁴ - 1] / 0.75% = $2,813,492

Mike's FV = $375 x [(1 + 0.75%)⁴¹⁴ - 1] / 0.75% = $1,052,612

then $1,052,612 x (1.09)⁷°⁵ = $2,008,940

Mike's FV = $500 x [(1 + 0.75%)⁹⁰ - 1] / 0.75% = $63,939

total = $2,008,940 + $63,939 = $2,072,879