Question

Alex is 31 years old and has lived in Los Alamos, New Mexico, for the last four years, where he works at the Los Alamos National

Laboratory (LANL). LANL provides employees with a 401(k) plan, and for every $1 an employee contributes (up to 9 percent of the
employee's salary), LANL contributes $3 (a 3-to-1 match). The plan provides a six-year graded vesting schedule. Alex is now in his fifth
year working for LANL, and his current-year salary is $190,000. Alex's marginal tax rate is 24 percent in 2023.
Answer the following questions relating to Alex's retirement savings in 2023. (Use Exhibit 13-2. Exhibit 13-3.)
Required:
a. Assume that over the past four years, Alex has contributed $45,000 to his 401(k) and his employer has contributed $115,000 to the
plan. The plan has an account balance of $175,000. What is Alex's vested account balance in his 401(k)?
b. Because Alex considers his employer's matching contributions "free money," he wants to maximize the amount of LANL's
contributions. What is the least amount Alex can contribute and still maximize LANL's contribution?
c. In need of cash to build a home theater, Alex withdrew $30,000 from his traditional 401(k) account. What amount of the withdrawal,
after taxes and penalties, will Alex have available to complete his project?
d. Assume that Alex contributes $10,000 to his traditional 401(k) account this year. Also assume that in 30 years, Alex retires (at age 61)
and withdraws the $10,000 contribution made this year and all the earnings generated by the contribution. Also assume that his
marginal tax rate at the time he retires is 24 percent. Ignore any prior or subsequent contributions to his plan. If Alex earns a 6
percent annual before-tax rate of return, what are his after-tax proceeds from the distribution?
e. Assume that Alex is 74 years old at the end of the year and retired. Further, assume his marginal tax rate is 24 percent. His account
balance in his traditional 401(k) was $1,250,000 at the end of last year. What is the minimum distribution Alex must receive from his
401(k) account for this year? If Alex receives a $43,000 distribution from his 401(k) account (his only distribution during the year).
what amount will he be able to keep after taxes and penalties (if any)?
Complete this question by entering your answers in the tabs below.
Required C Required D Required E
e. Assume that Alex is 74 years old at the end of the year and retired. Further, assume his marginal tax rate is 24 percent.
His account balance in his traditional 401(k) was $1,250,000 at the end of last year. What is the minimum distribution Alex
must receive from his 401(k) account for this year? If Alex receives a $43,000 distribution from his 401(k) account (his only
distribution during the year), what amount will he be able to keep after taxes and penalties (if any)?
Required A
Required B
Minimum distribution required= 49,000
After-tax proceeds=?

Answer 1

To calculate the difference between Alexx and Spenser's investments after 30 years, apply the future value formula with their respective interest rates and subtract Spenser's future value from Alexx's. Alexx's investment is compounded annually at 5%, and Spenser's at 4.75%, to account for the retirement fund's administrative fee.

To calculate how much more Alexx will have than Spenser after 30 years, we must apply the formula for future value with the different interest rates they will each receive. For Alexx, the future value will be calculated using a 5% interest rate while Spenser's future value will use a 4.75% rate, reflecting the 0.25% administrative fee taken by the retirement fund.

The formula to use for the future value of an investment is:

FV = PV (1 + r)^n

Where:

FV represents the future value of the investment.

PV is the present value or initial amount invested, which is $5,000.

r is the annual interest rate (0.05 for Alexx and 0.0475 for Spenser).

n is the number of years the money is invested, which is 30.

Calculating for both investors:

Alexx's Investment after 30 years: $5,000(1 + 0.05)^{30}

Spenser's Investment after 30 years: $5,000(1 + 0.0475)^{30}

Subtracting Spenser's future value from Alexx's will give us how much more Alexx has:

Alexx's FV - Spenser's FV

Follow these steps, and you will be able to determine the difference in the future value of their investments due to the varying interest rates.