Step-by-step explanation:
To calculate the future value of an investment with compound interest, we can use the formula:
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $2300, the annual interest rate (r) is 6.25% or 0.0625 (in decimal form), the interest is compounded annually (n = 1), and the number of years (t) is 9.
Substituting the given values into the formula, we have:
\[A = 2300 \left(1 + \frac{0.0625}{1}\right)^{1 \times 9}\]
Simplifying the expression inside the parentheses:
\[A = 2300 \left(1.0625\right)^9\]
Calculating the value of \((1.0625)^9\) gives:
\[A \approx 3768.30\]
Therefore, the investment will be worth approximately $3768.30 after 9 years.
