Step-by-step explanation:
To calculate the future value of the investment after 7 years, you can use the formula for compound interest:
\[FV = PV \times (1 + r - f)^t\]
Where:
- \(FV\) is the future value of the investment
- \(PV\) is the present value (initial investment)
- \(r\) is the annual rate of return (as a decimal)
- \(f\) is the annual expense ratio (as a decimal)
- \(t\) is the number of years
In this case:
- \(PV = $525\)
- \(r = 0.088\) (8.8% as a decimal)
- \(f = 0.014\) (1.4% as a decimal)
- \(t = 7\) years
Now you can plug these values into the formula to find the future value.
To calculate the worth of Mateo's investment after 7 years, we need to take into account the average annual rate of return and the expense ratio.
1. Calculate the annual growth of the investment: The average annual rate of return is 8.8%. To calculate the annual growth, we add 1 to the rate and convert it to a decimal: 1 + 0.088 = 1.088.
2. Calculate the net growth after accounting for the expense ratio: The expense ratio is 1.4%. To calculate the net growth, we subtract the expense ratio from 1: 1 - 0.014 = 0.986.
3. Calculate the total growth after 7 years: To calculate the total growth, we raise the net growth to the power of the number of years: 0.986^7.
4. Calculate the final worth of the investment: Multiply the initial investment of $525 by the total growth after 7 years.
Calculating the total growth after 7 years:
0.986^7 ≈ 0.8881
Calculating the final worth of the investment:
$525 * 0.8881 ≈ $465.35
Therefore, Mateo's investment would be worth approximately $465.35 after 7 years, taking into account the average annual rate of return of 8.8% and the expense ratio of 1.4%.
bye!! hope this helps!! <3 - sun
