How long would it take to double your principal in an account that pays 6.5% annual interest compounded continuously? round your answer to one decimal place?

It would take 10.7 years.

The formula for continuously compounded interest is:

where P is the principal, r is the interest rate as a decimal number, and t is the number of years.

Using our information we have:


We want to know when it will double the principal; therefore we substitute 2P for A and solve for t:


Divide both sides by P:


Take the natural log, ln, of each side to "undo" e:


Divide both sides by 0.065:

The first one is 2/3the second is 1/160the third is 4/125