Question

When you start your first job after graduating from Ohio State on January 1st, 2023, you saved a portion of your salary in your company's 401k savings plan. Your salary is $60,000 annually, of which you put 10% in the savings plan at the end of each year. (In reality, a portion is saved from each paycheck, but we will use annual deposits for simplicity.) Assume the savings plan earns 4% interest annually. Now it is four years later, January 1, 2027. Your company provides matching contributions to the savings plan on the first 5% of compensation that you contribute to the savings plan. For example, if you contribute 2% of your salary, your company will match that and deposit an amount equal to 2% of your salary, too. A total of 4% of your salary is deposited into the savings plan. Another example, if you contribute 30% of your salary, your company will only match the first 5% contributed and deposit an amount equal to 5% of your salary. A total of 35% of your salary is deposited into the savings plan.

a) What is the amount of each deposit "A" (A = your contribution+your employer's) on December 31st in 2023, 2024, 2025, and 2026 (today)?

ANSWER = 9000

b) What is the total amount of money that is in your savings plan account today?

ANSWER = 38218.18

c) Calculate the total amount of cash, excluding interest, that was actually taken out of your paycheck over the course of 4 years. Consider the following three scenarios (in parts d, e, f and g) independently of each other:

ANSWER = 24000

d) Scenario 1: For some reason, you stop contributing to your company's savings plan after the 4 deposits above, so the current amount in your savings plan (part b) earns interest without any additional contributions. What amount would be in your savings account in 2032 (6 years from today)?

ANSWER = 48358.18

e) Scenario 2: Let's say, you and your company contribute the same amount (part a) every year for the next 6 years until July 1, 2032 (10 deposits total). Now, how much would be in your savings account in 2032?

ANSWER =?

f) Scenario 3(Continuation of Scenario 2): While you are making these depositis into your 401k, you are also buying a $3,000 a year vacation, at the end of the year, on your Citi Double Cash Credit Card and NOT paying it off. The APR on your card is 25.74% (very real). You buy 6 vacations from 2026 -2032. After cashing your 401k, how much money do you have in 2032 if you decide to pay off your credit card in 2032?

ANSWER =?

g) Scenario 4: Consider your friend, who is employed by the same company, does not utilize the 401k savings plan. Instead, she puts her leftover income of $2,000 per year of into a savings account that earns 4% annual interest. After only 4 years, how much money has your friend missed out on if she had saved 5% of her salary per year with the 401k match? Assume your friend's salary is also $60,000 and would have saved 5% of her salary annually into the 4% interest earning 401k match program.

Answer 1

e) The deposit from the salary is 10% of the $60000 and now the company is matching with it. That means the company also making a $6000 deposit. The total payments made are equal to 10 and the interest rate is 4%

FV = Payment * ( 1 + Interest Rate )^{Total Years}

=FV(4%,10,-12000)
= $144073.29

The total amount after 10 years will be $144073.29 in the account.

f) A $3000 vacation expense has been incurred for a total of six years. The APR has been given as 25.74%

FV = Payment * ( 1 + Interest Rate )^{Total Years}
=FV(25.74%,6,-3000)
= $34408.12
The amount paid is $34408.12

Total saving is the account = $144073.29
144073.29 - 34408.12 = $109665.17

The funds available in the account is $109665.17

g) The person is putting $2000 at a 4% interest rate in another scheme.
=FV(4%,4,-2000)
= 8492.93

If she had put 5% of her salary in 401k with the matching from the company then the amount would have been $6000.
( 60000 * 0.05 ) = 3000
3000 + 3000 = 6000

=FV(4%,4,-6000)
= 25478.78

25478.78 - 8492.93 = 16985.86

She has missed out the gain of $16985.86 in a total of four years.