Find the time (in years) necessary for 1,000 to double if it is invested at a rate 6% compounded continuously. Round your answer to two decimal places.
A)1.16 years
B)11.55 years
C)1.39 years
D)11.90 years
E)11.58 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 money, $A = 2P$. Substituting the given values, we get $2(1000) = 1000e^{0.06t}$. Simplifying, we get $2 = e^{0.06t}$. Taking the natural logarithm of both sides gives $ln(2) = 0.06t$. Solving for $t$, we get $t = \frac{ln(2)}{0.06} \approx 11.55$ years.

Find the Time (In Years) Necessary for 1,000 to Double