Answer:
Explanation:
The formula for compound interest compounded continuously is given by:
where:
- \(A\) is the future value of the investment/loan, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(e\) is the mathematical constant approximately equal to 2.71828.
- \(r\) is the annual interest rate (as a decimal).
- \(t\) is the time the money is invested or borrowed for, in years.
In this case:
- \(P = $9600\)
- \(r = 0.031\) (3.1% expressed as a decimal)
- \(t = 4\) years
Plugging these values into the formula:
\[ A = 9600 \cdot e^{0.031 \cdot 4} \]
Let's calculate this:
\[ A \approx 9600 \cdot e^{0.124} \]
\[ A \approx 9600 \cdot 1.13298 \]
\[ A \approx 10865.088 \]
So, the value of Melanie's investment after 4 years, rounded to the nearest cent, is approximately $10,865.09.