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.