Final answer:
The final account balance after tax of a regular savings account is $22,940.52. The expected final account balance after tax of a 401(k) savings account is $16,058.36. The expected final account balance after tax of a Roth 401(k) savings account is $16,058.36.
Step-by-step explanation:
(a) To calculate the final account balance after tax of a regular savings account, we need to consider the long-term expected rate of return, the marginal tax rates, and the investment horizon. Since the investment horizon is 40 years and the long-term expected rate of return is 6%, we can use compound interest formula to calculate the final balance after tax:
Final Balance = Initial Investment * (1 + Long-term Rate of Return)^(Investment Horizon)
Final Balance = $3000 * (1 + 0.06)^40
Final Balance = $3000 * (1.06)^40
Final Balance = $3000 * 7.6468401
Final Balance = $22,940.52
(b) For a 401(k) savings account, the contribution is made before tax, and the tax is deferred until withdrawal. This allows for tax savings at the time of contribution. Since the marginal tax rate at the time of contribution is 30%, we can calculate the final balance after tax using the same formula:
Final Balance = (Initial Investment * (1 - Marginal Tax Rate at the Time of Contribution)) * (1 + Long-term Rate of Return)^(Investment Horizon)
Final Balance = ($3000 * (1 - 0.30)) * (1 + 0.06)^40
Final Balance = $2100 * 7.6468401
Final Balance = $16,058.36
(c) For a Roth 401(k) savings account, the contribution is made after tax, and no tax is paid on investment income or withdrawals. Since the marginal tax rate at the time of contribution is 30% and the marginal tax rate on investment income is 20%, we can calculate the final balance after tax using the same formula:
Final Balance = (Initial Investment * (1 - Marginal Tax Rate at the Time of Contribution)) * (1 + Long-term Rate of Return)^(Investment Horizon)
Final Balance = ($3000 * (1 - 0.30)) * (1 + 0.06)^40
Final Balance = $2100 * 7.6468401
Final Balance = $16,058.36