anonymous 4 years ago Interest formula P= Principle 1000 n = number of years 3 I = rate 5% m= ending balance 1157.63 1000 * (1+i) to the 3rd power = 1157.63 1000 * (1+.05) to the 3rd power =1157.63 1000 * (1.05 * 1.05 *1.05 ) = 1157.63 How do I solve for i if everything else is known? Thank you

1. anonymous

This was just an example. Assume I know everything else but the rate and want to determine it.

2. ash2326

We have Ending Balance = Principle*(1+Rate)^{Time in years} m=P*(1+i)^t to find i? $\frac{m}{p}=(1+i)^t$ take log boths sides $log_{10} \frac{m}{p}=t *log_{10}(1+i)$ $\frac{1}{t}log_{10} \frac{m}{p}=log_{10}(1+i)$ take anti log both sides $\large{1+i=10^{\frac{1}{t}log_{10} \frac{m}{p}}}$ or $\large{i=10^{\frac{1}{t}log_{10} \frac{m}{p}}-1}$

3. ash2326

or $i=(\frac{m}{p})^{\frac{1}{t}}-1$

4. anonymous

I think you have it, but I don't know how I would use it with the 1 over t power. I don't see how to do the math. Thanks

5. anonymous

Ah yes I should've realized it wasn't simple interest formula when he was cubing the time. lol

6. anonymous

Figured out how to use your formula with an exponential calculator, Thanks for your help. I had an Algebra teacher look at it and not be able to figure it out.