1. ## Compound interest formula

Fred invests an amount of money in an account by paying r% compound interest per annum. The amount of money doubles after n years.

I'm aware of the compound interest formula A=P(1+r/100)^n however I have no idea how to change it according to n.
Would I start off along the lines of 2A=p(1+r/100)^n?

2. (1 + r)^n = 2
n = log(2) / log(1 + r)

Example: r = .06 (6%)
n = log(2) / log(1.06) = 11.89566.... ; not quite 12 years

3. Can't use a method that utilises logs

4. Originally Posted by Mukilab
Can't use a method that utilises logs
Well, too bad so sad: that's the only way to solve directly.

5. Its not. I know that for a fact.

6. What about simplifying it so you have the equation pertaining to r

7. r = 2^(1/n) - 1

SO?

IF you know it as a fact: then SHOW US.

8. I know as a fact because it is impossible a question pertaining to logs would show up in a paper that specifies to a certain age that has never previously learned logs and 8 years later they still are not teaching logs to this age group!

9. Originally Posted by Wilmer
r = 2^(1/n) - 1

SO?

IF you know it as a fact: then SHOW US.
Would it not be

$\displaystyle 100(^{n}\sqrt{2}-1)$

10. Originally Posted by Mukilab
I know as a fact because it is impossible a question pertaining to logs would show up in a paper that specifies to a certain age that has never previously learned logs and 8 years later they still are not teaching logs to this age group!
Have a good day, Mukilab.

11. Instead of separating Total from investment can I do 2p=p(1+r/100)^n?

12. Originally Posted by Mukilab
Instead of separating Total from investment can I do 2p=p(1+r/100)^n?
That is what Wilmer posted in post 2 (except he cancelled out p which is the next step)

Originally Posted by Mukilab
Fred invests an amount of money in an account by paying r% compound interest per annum. The amount of money doubles after n years.

I'm aware of the compound interest formula A=P(1+r/100)^n however I have no idea how to change it according to n.
Would I start off along the lines of 2A=p(1+r/100)^n?
I don't know how you'd solve for n without using logarithms, I doubt it's even possible, perhaps they use logarithms without knowing it?