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.

Answer 1

The difference in account balances after 3 years is $3,985.97

Step-by-step explanation:

To determine the difference in account balances after 3 years, we can calculate the values for both the IRA and 401k accounts.

For the IRA, the initial investment of $5,000 will grow at a rate of 4.5% compounded annually for 3 years.

Using the compound interest formula, the future value of the IRA account after 3 years will be $15,685.13.

For the 401k, the employer matches 30% of the annual contributions, so the total annual contributions will be $5,000 + 30% of $5,000 = $6,500

The annual contribution of $6,500 will grow at a rate of 3.5% compounded annually for 3 years.

Using the compound interest formula, the future value of the 401k account after 3 years will be $19,671.10.

The difference in account balances after 3 years will be $19,671.10 - $15,685.13 = $3,985.97.

Answer 2

To calculate the difference in account balances after 3 years, you can use the formulas for compound interest. The IRA has a rate of 4.5% and the 401k has a rate of 3.5% with an employer match of 30%. After calculating the values for both accounts after 3 years and subtracting the IRA value from the 401k value, the difference in account balances is $5,989.15.

Step-by-step explanation:

To determine the difference in account balances after 3 years, we need to calculate the value of both the IRA and the 401k after 3 years and then subtract the IRA value from the 401k value.

For the IRA, we use the formula for compound interest: A = P(1+r)^n

Given the IRA has a rate of 4.5%, compounded annually, we have A = $5,000(1+0.045)^3 = $15,685.13

For the 401k, we consider that the employer matches 30% of the annual contributions and the rate is 3.5%, compounded annually.

The annual contribution to the 401k is $5,000 and the employer matches 30% of that, so the total contribution is $5,000 + $5,000(0.3) = $6,500.

The value of the 401k after 3 years is A = $6,500(1+0.035)^3 = $21,674.28

The difference in account balances after 3 years is $21,674.28 - $15,685.13 = $5,989.15.