Question

A recently-graduated college student is deciding whether to contribute $5,000 per year to a 401k at their job or an ira. the terms of both are: ira: 4.5% rate, compounded annually, with a total value of $15,685.13 after 3 years 401k: employer matches 30% of annual contributions, with a 3.5% rate, compounded annually determine the difference in account balances after 3 years. a spreadsheet was used to calculate the correct answer. your answer may vary slightly depending on the technology used. a.the first offer is greater by $4,505.34. b.the second offer is greater by $4,505.34. c.the first offer is greater by $154.00. d.the second offer is greater by $154.00

Answer 1

After calculating the future values using the compound interest formula, the 401k balance after three years is greater than the IRA by $5,207.34, based on the 30% employer match and the respective interest rates of 3.5% for the 401k and 4.5% for the IRA.

Step-by-step explanation:

We are tasked with determining which option yields a greater account balance after three years: contributing to an IRA with a 4.5% rate compounded annually or a 401k with a 3.5% rate and a 30% employer match.

For the IRA, the future value (FV) can be calculated using the compound interest formula FV = P(1 + r)n, where P is the principal, r is the annual interest rate, and n is the number of years. We are given that $15,685.13 is the value after 3 years, so there's no need to calculate for the IRA.

The 401k contribution is $5,000 per year plus the employer's 30% match, which is $1,500, resulting in a total annual contribution of $6,500. Using the compound interest formula, the future value of the 401k after 3 years is:
FV = 6,500(1 + 0.035) + 6,500(1 + 0.035)2 + 6,500(1 + 0.035)3

Calculating each term separately and summing up gives:
FV = 6,500(1.035) + 6,500(1.071225) + 6,500(1.107886125)
= 6,727.75 + 6,963.46 + 7,201.26
= 20,892.47

To find the difference in balances, subtract the IRA value from the 401k value: $20,892.47 - $15,685.13 = $5,207.34.

Therefore, the correct answer is that the second offer (401k) is greater by $5,207.34.

Answer 2

b. The second offer is greater by $4,505.34.Considering the time value of money, the 401k option, with its employer match, demonstrates its advantage in generating a higher account balance over the specified duration compared to the IRA's interest rate alone.

Step-by-step explanation:

After careful calculation, it's evident that the 401k with the employer match generates a greater account balance difference of $4,505.34 after three years compared to the IRA. This outcome is primarily due to the advantageous combination of the employer's 30% match on contributions and the 3.5% compounded annually rate.

The employer match in the 401k significantly boosts the total amount saved, contributing to a larger balance than the IRA with a 4.5% interest rate compounded annually. Even though the IRA had a higher interest rate, the added benefit of the employer's contribution in the 401k considerably outweighs the difference in interest rates over the three-year period.

Considering the time value of money, the 401k option, with its employer match, demonstrates its advantage in generating a higher account balance over the specified duration compared to the IRA's interest rate alone. This highlights the significant impact that employer matching programs can have on accumulating retirement savings over time.

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