How many years are required for an investment to double in value if it is appreciating at the rate of 11​% compounded​ continuously?

Question

 At 11 % compounded continuously, the investment doubles in how many years

Answer 1

The formula for continuous compound interest is A=Pe^rt

 

t is the number of years

r is the interest rate as a decimal

e is the number roughly equal to 2.7

P is the starting amount

A is the final amount

 

We want A=2P, meaning the initial amount has doubled. So we want to solve the following equation for t:

 

2P=Pe^rt

 

We start by dividing both sides by P

 

2=e^rt

 

Now take the natural log to get t out of the exponent

 

ln(2)=rt

 

Finally, divide by r

 

ln(2)/r=t

 

plugging in 0.11 for r, we find:

 

t=ln(2)/0.11

 

ln(2)/0.11=6.3 years