Solve the problem. Round your answer to three decimals.
-How long will it take for an investment to triple in value if it earns 8.5% compounded continuously?
A) 12.925 years
B) 8.155 years
C) 6.462 years
D) 13.797 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 triple the investment, $A/P = 3$. Substituting the given values and solving for $t$, we get $3 = e^{0.085t}$. Taking the natural logarithm of both sides gives $ln(3) = 0.085t$, and solving for $t$ gives $t = ln(3)/0.085 \approx 12.925$ years.

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