Question

In 2022, Nina contributes 8 percent of her $158,000 annual salary to her 401(k) account. She expects to earn a 9 percent before-tax rate of return. Assuming she leaves this (and any employer contributions) in the account until she retires in 30 years, what is Nina's after-tax accumulation from her 2022 contributions to her 401(k) account? (Use Table 1, Table 2.)

Note: Round your intermediate calculations and final answers to the nearest whole dollar amount.

a. Assume Nina's marginal tax rate at retirement is 30 percent.

After tax proceeds from distribution?

b. Assume Nina's marginal tax rate at retirement is 20 percent.

After tax proceeds from distribution?

c. Assume Nina's marginal tax rate at retirement is 40 percent.

After tax proceeds from distribution?

Answer 1

To determine Nina's after-tax accumulation from her 401(k) contributions in 2022, calculate her contribution, determine the accumulated value over 30 years with a 9% return, and apply the relevant marginal tax rates of 30%, 20%, and 40% at retirement to find the after-tax proceeds.

Step-by-step explanation:

To calculate the after-tax accumulation from Nina's 2022 contributions to her 401(k) account, we first determine her contribution amount and then calculate the accumulation at a 9% before-tax rate of return over 30 years. Next, we calculate the after-tax proceeds assuming different marginal tax rates at retirement.

Nina contributes 8% of her $158,000 annual salary to her 401(k) which equals $158,000 * 0.08 = $12,640. Using the compound interest formula, the future value of this contribution over 30 years at a 9% annual return is $12,640 * (1 + 0.09)^30.

• For a 30% marginal tax rate: $12,640 * (1 + 0.09)^30 * (1 - 0.30)
• For a 20% marginal tax rate: $12,640 * (1 + 0.09)^30 * (1 - 0.20)
• For a 40% marginal tax rate: $12,640 * (1 + 0.09)^30 * (1 - 0.40)

These calculations will provide the after-tax proceeds from distribution for each marginal tax rate scenario.

Answer 2

Nina's after-tax accumulation from her 2022 contributions to her 401(k) depends on her marginal tax rate at retirement. By computing the future value of her contributions with a 9 percent rate of return over 30 years, and then adjusting for tax rates of 30%, 20%, and 40%, we can calculate her different possible after-tax accumulations.

Step-by-step explanation:

In 2022, Nina contributes 8 percent of her $158,000 annual salary to her 401(k) account. This amounts to $12,640 for the year. Assuming a 9 percent before-tax rate of return and leaving it in the account for 30 years, we can use the future value formula to calculate the amount before considering taxes: FV = PV x (1 + r)^n, where PV (present value) is $12,640, r (rate) is 0.09, and n (number of periods) is 30.

Therefore, FV = $12,640 x (1 + 0.09)^30. After calculating FV, we subtract the tax impact at retirement to find the after-tax accumulation for different tax rates.

• a. With a marginal tax rate of 30 percent, after-tax accumulation is FV x (1 - 0.30).
• b. With a marginal tax rate of 20 percent, after-tax accumulation is FV x (1 - 0.20).
• c. With a marginal tax rate of 40 percent, after-tax accumulation is FV x (1 - 0.40).