Question

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

Answer 1

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

Answer 2

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
\[\large{i=10^{\frac{1}{t}log_{10} \frac{m}{p}}-1}\]

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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.