How much will $100 grow to if invested at a continuously compounded interest rate of 10.75% for 8 years?
Here are several tools to calculate compound interest:
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To calculate the future value of an investment with continuously compounded interest, you can use the formula:
FV = P * e^(rt)
Where:
FV = Future Value
P = Principal (initial investment)
e = Euler's number (approximately 2.71828)
r = Interest rate
t = Time (in years)
In this case, the principal is $100, the interest rate is 10.75% (or 0.1075 as a decimal), and the time is 8 years.
Plugging these values into the formula:
FV = $100 * e^(0.1075 * 8)
First, calculate the exponent:
0.1075 * 8 = 0.86
Next, calculate e^(0.86) using a calculator or a math library. Let's assume the result is approximately 2.36.
Finally, calculate the future value:
FV = $100 * 2.36 = $236
Therefore, if you invest $100 at a continuously compounded interest rate of 10.75% for 8 years, it will grow to approximately $236.