Question

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?

Answer 1

11 years

Explanation:

Answer 2

It would take 10.7 years.

The formula for continuously compounded interest is:

`A=Pe^(rt)`
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:

`A=Pe^(0.065t)`

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

`2P=Pe^(0.065t)`

Divide both sides by P:

`(2P)/(P)=(Pe^(0.065t))/(P) \\ \\2=e^(0.065t)`

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

`ln(2)=\ln{e^(0.065t)} \\ \\0.6931471806=0.065t`

Divide both sides by 0.065:

`(0.6931471806)/(0.065)=(0.065t)/(0.065) \\ \\10.7\approx t`