To calculate the future value of an investment with continuous compounding, you can use the formula:
\[ FV = P \times e^{rt} \]
where:
- \(FV\) is the future value,
- \(P\) is the principal amount (initial investment),
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the time in years,
- \(e\) is the base of the natural logarithm (approximately equal to 2.71828).
In this case, you have:
- \(P = 803.00\)
- \(r = 4.00% = 0.04\)
- \(t = 5\) years
Now you can plug these values into the formula:
\[ FV = 803.00 \times e^{(0.04 \times 5)} \]
First, calculate \(0.04 \times 5\):
\[ 0.04 \times 5 = 0.20 \]
Now calculate \(e^{0.20}\):
\[ e^{0.20} \approx 1.2214 \]
Now calculate the future value:
\[ FV = 803.00 \times 1.2214 \approx 980.44 \]
Therefore, the future value of the investment in five years is approximately $980.44.