Solve the problem. Round your answer to three decimals.
-How long will it take for an investment to double in value if it earns 9.25% compounded continuously?
A) 7.493 years
B) 3.747 years
C) 7.781 years
D) 11.877 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. To double the investment, $A/P = 2$, so we solve $2 = e^{0.0925t}$. Taking the natural logarithm of both sides gives $ln(2) = 0.0925t$, and solving for $t$ gives $t = \frac{ln(2)}{0.0925} \approx 7.493$ years.

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