an electrician is 27 years old and starting a 401k. the employee plans to invest $350 per month with an…

an electrician is 27 years old and starting a 401k. the employee plans to invest $350 per month with an expected interest rate of 3.5%, compounded monthly. after 30 years of working, the employee wants to have $200,000 in the retirement account. what is the difference between the actual balance and the employees goal?\na spreadsheet was used to calculate the correct answer. your answer may vary slightly depending on the technology used.\nthe actual balance is $29,340.64 higher than the goal.\nthe actual balance is $29,340.64 lower than the goal.\nthe actual balance is $22,394.46 higher than the goal.\nthe actual balance is $22,394.46 lower than the goal.

an electrician is 27 years old and starting a 401k. the employee plans to invest $350 per month with an expected interest rate of 3.5%, compounded monthly. after 30 years of working, the employee wants to have $200,000 in the retirement account. what is the difference between the actual balance and the employees goal?\na spreadsheet was used to calculate the correct answer. your answer may vary slightly depending on the technology used.\nthe actual balance is $29,340.64 higher than the goal.\nthe actual balance is $29,340.64 lower than the goal.\nthe actual balance is $22,394.46 higher than the goal.\nthe actual balance is $22,394.46 lower than the goal.

Answer

Explanation:

Step1: Define annuity formula variables

Let $P = 350$ (monthly payment), $r = 0.035$ (annual rate), $n = 12$ (compounds/year), $t = 30$ (years).

Step2: Calculate monthly rate & total periods

Monthly rate: $i = \frac{r}{n} = \frac{0.035}{12}$ Total periods: $N = n \times t = 12 \times 30 = 360$

Step3: Compute future value of annuity

Use future value formula: $$FV = P \times \frac{(1+i)^N - 1}{i}$$ Substitute values: $$FV = 350 \times \frac{\left(1+\frac{0.035}{12}\right)^{360} - 1}{\frac{0.035}{12}}$$ Calculate $\left(1+\frac{0.035}{12}\right)^{360} \approx 2.8533$ $$FV = 350 \times \frac{2.8533 - 1}{\frac{0.035}{12}} = 350 \times \frac{1.8533}{0.0029167} \approx 229340.64$$

Step4: Find difference vs goal

Goal = $200000$, so difference: $229340.64 - 200000 = 29340.64$

Answer:

The actual balance is $29,340.64 higher than the goal.