Compound Interest Formula and Natural Logarithms

[adillhoff]

Homework Statement

Solve the compound interest formula for t by using natural logarithms.

Homework Equations

$$A=P(1+\frac{r}{n})^{nt}$$

The Attempt at a Solution

I start by dividing both sides by P.
I then take the natural log of both sides and end up with

$$ln(\frac{A}{P})=nt * ln(1+\frac{r}{n})$$

I isolate t to one side by first dividing by $$ln(\frac{A}{P})$$ then by t.

I end up with $$t=\frac{n*ln(1+\frac{r}{n})}{ln(\frac{A}{P})}$$

I don't believe this is the correct answer. I can't seem to see which step I overlooked at the moment. Any help would be greatly appreciated.

 

[Tide]

You made a simple algebraic mistake in the step where you solve for t. You need to divide by n*ln(1+r/n).

 

[adillhoff]

Of course. I knew I missed something simple. Thanks for the reply.