Questions: An employer will do a 50% match on your investment to a 401 k retirement plan. If you decide to contribute a monthly amount of 220, how much should be in the account after 15 years? The interest rate is fixed at 2.05%.

Solution Steps

To solve this problem, we need to calculate the future value of a series of monthly contributions to a retirement account, considering both the employer's match and the interest rate. First, determine the total monthly contribution by adding the employer's match to your contribution. Then, use the future value of an annuity formula to calculate the total amount in the account after 15 years, taking into account the fixed interest rate compounded monthly.

The total monthly contribution, including the employer's match, is calculated as follows: \[ \text{Total Monthly Contribution} = \text{Monthly Contribution} \times (1 + \text{Employer Match Percentage}) = 220 \times (1 + 0.5) = 220 \times 1.5 = 330 \]

The annual interest rate is converted to a monthly rate: \[ \text{Interest Rate (Monthly)} = \frac{\text{Interest Rate (Annual)}}{12} = \frac{0.0205}{12} \approx 0.0017083 \]

The total number of months over 15 years is: \[ \text{Months} = 15 \times 12 = 180 \]

Using the future value of an annuity formula, we find the total amount in the account after 15 years: \[ \text{Future Value} = \text{Total Monthly Contribution} \times \left( \frac{(1 + \text{Interest Rate (Monthly)})^{\text{Months}} - 1}{\text{Interest Rate (Monthly)}} \right) \] Substituting the values: \[ \text{Future Value} = 330 \times \left( \frac{(1 + 0.0017083)^{180} - 1}{0.0017083} \right) \approx 69476.5665 \]

Final Answer