Compounding Interest: solving 175 = 100(1 + 0.08/12)^(12t)

[Remmy]

I'm in quite a rut right now. I have a bunch of homework due tomorrow but I can't seem to understand the method of how to solve a particular type of problem. I need to find out in order to complete the rest of the problems so I plead anyone to help me...D: I'm desperate.

That is what the problem looks like. I'm trying to find how long it will take to get 175 if it is compunded monthly. Y'see, I already put everything in the equation. I just can't seem to understand HOW to get the t in the exponent. How do I solve for t? It's an exponent...

So I thought, "Maybe I should use log..."

And, if I used the log of both sides, "12t" would drop into the front of 100 on that side of the equation, right? But it didn't work.

Can anyone help me? Please, please, please.

Thanks so much. I appreciate it.

 

[galactus]

It'll work. What are you doing?.

\(\displaystyle \L\\175=100\left(1+\frac{0.08}{12}\right)^{12t}\)

\(\displaystyle \L\\\frac{7}{4}=\left(\frac{151}{150}\right)^{12t}\)

Property of logs:

\(\displaystyle \L\\ln(\frac{7}{4})=12tln\left(\frac{151}{150}\right)\)

Now, can you finish solving for t?. Divide through by 12ln(151/150)