To determine how much a principal of [tex]$3500 will be worth after 8 years when invested at an annual interest rate of 6.25% and compounded annually, we can employ the formula for compound interest:
\[ A = P (1 + r/n)^{nt} \]
where:
- \( A \) is the future value of the investment/loan, including interest.
- \( P \) is the principal investment amount (the initial deposit or loan amount).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed for.
Given:
- \( P = 3500 \) dollars
- \( r = 0.0625 \)
- \( n = 1 \) (since the interest is compounded annually)
- \( t = 8 \) years
We can simplify the general formula to the form appropriate for annual compounding, which is:
\[ A = P (1 + r)^t \]
Substitute the given values into the formula:
\[ A = 3500 (1 + 0.0625)^8 \]
First, calculate the value inside the parentheses:
\[ 1 + 0.0625 = 1.0625 \]
Next, raise this value to the power of 8:
\[ 1.0625^8 \approx 1.623313 \]
Now multiply this result by the principal amount:
\[ 3500 \times 1.623313 \approx 5684.595332 \]
Rounding this resulting future value to the nearest dollar gives us:
\[ 5685 \]
Therefore, after 8 years, the investment will be worth approximately $[/tex]5685.
