Question

An employee contributes $75 each month to her 401(k). What will be the value of her 401(k) after the 240th deposit (20 years) if the per annum rate of return is assumed to be 12% compounded monthly?

Answer 1

To calculate the value of the 401(k) after 240 deposits (20 years), you can use the formula for compound interest. Using the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal investment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years, you can plug in the values to find the answer.

Step-by-step explanation:

To calculate the value of the 401(k) after the 240th deposit, we can use the formula for compound interest:

Formula: A = P(1 + r/n)^(nt)

Where:

• A is the future value of the investment
• P is the principal investment ($75 per month)
• r is the annual interest rate (12%)
• n is the number of times the interest is compounded per year (12 times for monthly compounding)
• t is the number of years (20 years)

Using these values, the formula becomes:

A = 75(1 + 0.12/12)^(12*20)

Calculating this expression will give us the value of the 401(k) after 20 years.

Answer 2

The value of her 401(k) will be 2,160 compounded monthly.