Solve the problem.
-Suppose that $8000 is invested at an interest rate of 5.5% per year,compounded continuously.How long would it take to double the investment?
A)13.6 yr
B)2 yr
C)12.6 yr
D)11.6 yr

Question

Quizplus · Accepted Answer

The formula for continuous compounding is: $A=P\cdot e^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal, $r$ is the interest rate, and $e$ is Euler's constant.

Let's use this formula to solve for $t$ when the investment doubles:
\begin{align*}
2P &= P\cdot e^{rt} \
2 &= e^{rt} \
\ln 2 &= rt \
t &= \frac{\ln 2}{r}
\end{align*}

Now we can substitute in the given values:
\begin{align*}
t &= \frac{\ln 2}{0.055} \
&\approx 12.6\ 	ext{years}
\end{align*}

So the answer is C) 12.6 yr.

Solve the Problem. -Suppose That $8000 Is Invested at an Interest Rate of Interest