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?
B) Amount in account at age 67?
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
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
