Future Value of Continuous Compounding with 10% Interest | CTFA Exam Answer

Calculate the Future Value of an Initial Investment with Continuous Compounding

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Question

With continuous compounding at 10 percent for 30 years, the future value of an initial investment of $2,000 is closest to:

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A. B. C. D.

B

To calculate the future value of an investment with continuous compounding, we can use the formula:

FV = Pe^(rt)

Where FV is the future value, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time period in years.

In this case, P = $2,000, r = 10%, and t = 30 years. Plugging these values into the formula, we get:

FV = 2000e^(0.1030) FV = 2000*e^3

Using a calculator, we can find that e^3 is approximately equal to 20.0855. Multiplying this by $2,000 gives us:

FV = $2,000 * 20.0855 FV = $40,171.00

Therefore, the closest answer choice is B. $40,171.

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