Answer:
To calculate the future value of an investment compounded continuously, we can use the formula:
Future Value = P * e^(rt)
Where:
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Period (in years)
Given:
P = $400
r = 2.6% = 0.026 (as a decimal)
t = 7 years
1. Calculate the future value:
Future Value = $400 * e^(0.026 * 7)
2. Evaluate the exponential part:
Using a scientific or online calculator, evaluate e^(0.026 * 7). The result is approximately 1.1923.
3. Multiply the principal amount by the exponential part:
Future Value = $400 * 1.1923
4. Calculate the future value:
Future Value = $476.92
Therefore, the future value of $400 invested at an annual interest rate of 2.6%, compounded continuously for seven years, is approximately $476.92.
