Final answer:
The value of Katie's 401k at retirement can be calculated using the future value of an annuity formula, considering her monthly contributions, the annual interest rate compounded monthly, and the duration of the investment. The formula demonstrates the significant impact that compound interest has on long-term savings.
Step-by-step explanation:
The question asks about the future value of a 401k retirement savings account with a starting age of 25 for the contributions, a retirement age of 65, a monthly contribution of $150, and an annual interest rate of 7.8% compounded monthly. To calculate this, we use the future value of an annuity formula which is given by:
FV = P × { [(1 + r)n - 1] / r }
Where:
- FV is the future value of the investment
- P is the monthly contribution ($150)
- r is the monthly interest rate (7.8% annual rate divided by 12)
- n is the total number of contributions (40 years multiplied by 12 months/year)
Using these values we get:
FV = 150 × { [(1 + 0.078/12)(40×12) - 1] / (0.078/12) }
= 401000
This is the total amount Katie will have in her 401k when she retires at age 65.
The power of compound interest significantly affects the growth of investments over time, and the earlier the saving starts the more substantial the future value will be due to the interest compounding over a longer period.