How Do You Algebraically Solve for n in Compound Interest Equations?

[e^(i Pi)+1=0]

Homework Statement

125,000=79,770.26(1+$\frac{.045}{n}$)¹⁰ⁿ

Homework Equations

The Attempt at a Solution

I'm not sure how to use a logarithm with this, or if it's even possible. I know that n=12, I just don't know how to solve for it.

 

[D H]

I know that n=12, I just don't know how to solve for it.

n = 12 is a solution for sufficiently large values of 12. n=12 (exactly) is not a solution. n≈12.06655246 is a solution.

You can't solve this analytically. You will need to resort to numerical techniques.

 

[e^(i Pi)+1=0]

Thanks, I wasn't sure if I was missing something. It's not exactly 12 here because the 79,770.26 is rounded.

 

[Joffan]

79,770.62 is closer, and 79,770.63 is closer still for n=12.

 

[Mentallic]

n = 12 is a solution for sufficiently large values of 12

 

[Curious3141]

n = 12 is a solution for sufficiently large values of 12.

Nice!