Questions: An employee is 25 years old and starting a 401 k plan. The employee is going to invest 150 each month. The account is expected to earn 5.5% interest, compounded monthly. What is the account balance, rounded to the nearest dollar, after two years? A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used. 3,976 3,796 6,675 6,765

An employee is 25 years old and starting a 401 k plan. The employee is going to invest 150 each month. The account is expected to earn 5.5% interest, compounded monthly. What is the account balance, rounded to the nearest dollar, after two years?

A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
3,976
3,796
6,675
6,765

Transcript text: An employee is 25 years old and starting a 401 k plan. The employee is going to invest $\$ 150$ each month. The account is expected to earn $5.5 \%$ interest, compounded monthly. What is the account balance, rounded to the nearest dollar, after two years? A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used. $\$ 3,976$ $\$ 3,796$ $\$ 6,675$ $\$ 6,765$

Solution

Solution Steps

To solve this problem, we need to use the future value of an annuity formula, which accounts for regular monthly contributions and compound interest. The formula is:

\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]

where:

$ P $ is the monthly contribution (\$150)
$ r $ is the monthly interest rate (annual rate / 12)
$ n $ is the total number of contributions (number of years $\times$ 12)

We will plug in the given values and compute the future value.

Step 1: Define Variables

Let:

$ P = 150 $ (monthly contribution)
$ r = \frac{5.5}{100} = 0.055 $ (annual interest rate)
$ n = 2 $ (years)

Step 2: Calculate Monthly Interest Rate and Total Months

The monthly interest rate is calculated as: \[ r_{monthly} = \frac{r}{12} = \frac{0.055}{12} \approx 0.0045833 \] The total number of contributions over 2 years is: \[ n_{total} = n \times 12 = 2 \times 12 = 24 \]

Step 3: Calculate Future Value of Annuity

Using the future value of an annuity formula: \[ FV = P \times \left( \frac{(1 + r_{monthly})^{n_{total}} - 1}{r_{monthly}} \right) \] Substituting the values: \[ FV = 150 \times \left( \frac{(1 + 0.0045833)^{24} - 1}{0.0045833} \right) \approx 3796.2840 \]

Step 4: Round Future Value

Rounding the future value to the nearest dollar gives: \[ FV_{rounded} = 3796 \]