Question

Shirley and Mabel both started work at the same company on the same day. Shirley decided to immediatelv contribute to the 401K that the company offers. Mabel on the other hand waited five years before starting to contribute to the 401K. On their 25th work anniversary let's fieure out the value of Shirley's and Mabel's 401K plans? Shirley contributed $75 per month to the 401K for 25 years. The 401K paid 6% compounded monthly. So, after 25 years of monthly contributions what is the value of Shirley's 401K?

Answer 1

Shirley's 401K value after 25 years of monthly $75 contributions with a 6% annual interest rate compounded monthly is $49,378.05, calculated using the future value of an annuity formula.

Step-by-step explanation:

To calculate the value of Shirley's 401K after 25 years of contributing $75 every month with an interest rate of 6% compounded monthly, we can use the future value of an annuity formula:

FV = P × ((1 + r)^n - 1) / r

Where:

• FV is the future value of the annuity.
• P is the periodic payment amount ($75 in this case).
• r is the monthly interest rate (6% per year or 0.06, divided by 12).
• n is the total number of payments (25 years × 12 months per year).

Firstly, we convert the annual interest rate to a monthly rate:

r = annual interest rate / number of compounding periods per year
= 0.06 / 12
= 0.005

Next, we calculate the total number of payments:

n = number of years × number of compounding periods per year
= 25 × 12
= 300

Then, we plug these figures into the formula:

FV = $75 × ((1 + 0.005)^300 - 1) / 0.005

Calculation:

FV = $75 × ((1.005)^300 - 1) / 0.005
= $75 × (4.291870 - 1) / 0.005
= $75 × 3.291870 / 0.005
= $75 × 658.374
= $49,378.05

After 25 years, the final value of Shirley's 401K is $49,378.05.