Question

In 2022, Nitai (age 40) contributes 8 percent of his $158,000 annual salary to a Roth 401(k) ) account sponsored by his employer, AY Incorporated. AY Incorporated matches employee contributions to the employee's traditional 401(k) account dollar-for-dollar up to 8 percent of the employee's salary. Nital expects to earn a 9 percent before-tax rate of return. Assume he leaves the contributions in the Roth 401(k) and traditional 401(k) accounts until he retires in 30 years and that he makes no additional contributions to either account. What are Nitai's after-tax proceeds from the Roth 401(k) and traditional 401(k) accounts after he receives the distributions, assuming his marginal tax rate at retirement is 30 percent? (Use Table 1. Table 2.) Note: Round your intermediate calculations and final answers to the nearest whole dollar amount.

Answer 1

To calculate Nitai's after-tax proceeds from the Roth 401(k) and traditional 401(k) accounts, we need to calculate the contributions, growth, distributions, and taxes for each account.

Step-by-step explanation:

To calculate Nitai's after-tax proceeds from the Roth 401(k) and traditional 401(k) accounts, we can follow these steps:

1. Calculate the amount contributed to each account by Nitai. 8% of Nitai's annual salary of $158,000 is $12,640.
2. Calculate the amount matched by AY Incorporated. AY Incorporated matches dollar-for-dollar up to 8% of the employee's salary, so they will match Nitai's contribution of $12,640.
3. Calculate the growth of the accounts over 30 years. Using a 9% before-tax rate of return, the amount in both accounts will grow.
4. Calculate the distributions Nitai receives after retiring. The distributions will be taxed at a marginal tax rate of 30%.
5. Calculate the after-tax proceeds by subtracting the taxes from the distributions.

Using these calculations, the after-tax proceeds from both the Roth 401(k) and traditional 401(k) accounts can be determined.

Answer 2

To calculate Nitai's after-tax proceeds from the Roth 401(k) and traditional 401(k) accounts, we need to consider the contributions, employer match, rate of return, and taxes. Nitai's after-tax proceeds from the Roth 401(k) account will be $167,456, while the after-tax proceeds from the traditional 401(k) account will be $117,219.

Step-by-step explanation:

To calculate Nitai's after-tax proceeds from the Roth 401(k) and traditional 401(k) accounts, we need to consider the contributions, employer match, rate of return, and taxes.

• For the Roth 401(k) account, Nitai contributes 8% of his $158,000 annual salary, which is $12,640. This is after-tax contributions, so there will be no taxes when he receives the distributions.
• For the traditional 401(k) account, Nitai's employer matches his contributions dollar-for-dollar up to 8% of his salary, which is also $12,640. This is a pre-tax contribution, so it will be taxed when he receives the distributions.
• To calculate the after-tax proceeds, we need to consider the rate of return. Nitai expects to earn a 9% before-tax rate of return on both accounts. This means that his investments will grow by 9% each year.
• Finally, we need to consider the taxes at retirement. Nitai's marginal tax rate at retirement is 30%. This means that when he receives distributions from the traditional 401(k) account, 30% will be deducted as taxes.

Using these calculations, Nitai's after-tax proceeds from the Roth 401(k) account will be the total contributions plus the growth over 30 years, which is
`12,640 + (12,640 * 0.09)^30`

= $167,456.

For the traditional 401(k) account, the contributions will be the same as the Roth 401(k) account, but the growth will be taxed at 30% when he receives the distributions.

So the after-tax proceeds will be
`12,640 + (12,640 * 0.09)^30 - (12,640 * 0.09)^30 * 0.30`

= $117,219.