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

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To solve for n in the compound interest equation 125,000=79,770.26(1+(.045/n))^10n, analytical methods are not effective, and numerical techniques are recommended. While n=12 is a close approximation, the exact solution is approximately n=12.06655246 due to rounding in the initial values. The discussion highlights the importance of recognizing that n=12 is not an exact solution but works for sufficiently large values. The rounding of 79,770.26 affects the accuracy, indicating that slightly adjusted values yield closer results. Numerical methods are essential for precise solutions in such equations.
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Homework Statement


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

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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.
 
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e^(i Pi)+1=0 said:
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.
 
Thanks, I wasn't sure if I was missing something. It's not exactly 12 here because the 79,770.26 is rounded.
 
79,770.62 is closer, and 79,770.63 is closer still for n=12.
 
D H said:
n = 12 is a solution for sufficiently large values of 12

:smile:
 
D H said:
n = 12 is a solution for sufficiently large values of 12.

Nice! :biggrin:
 

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