If $P is invested for n years at 6% compounded continuously, the rate at which the future value is growing is . In how many years will the future value double? Round your answer to one decimal place.
A) 18.3 years
B) 13.6 years
C) 11.6 years
D) 20.3 years
E) 16.6 years

Question

If $P is invested for n years at 6% compounded continuously, the rate at which the future value is growing is  . In how many years will the future value double? Round your answer to one decimal place. ​
A) 18.3 years 
B) 13.6 years 
C) 11.6 years 
D) 20.3 years 
E) 16.6 years

Quizplus · Accepted Answer

If the rate at which the future value is growing is $r$, then we know that the future value after $n$ years is given by:

$$FV=P\cdot e^{rn}$$

We want to find $n$ such that $FV=2P$. Substituting $FV=2P$ and $r=0.06$ gives:

$$2P=P\cdot e^{0.06n} \Rightarrow e^{0.06n}=2 \Rightarrow 0.06n=\ln 2 \Rightarrow n\approx 11.6$$

Therefore, the answer is (C) 11.6 years.

If $P Is Invested for N Years at 6% Compounded