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Name: Loretta S
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For compound interest that equation is T=P(1+r)to the n power my question is...What is a short cut to find the answer for n besides guess and check?

ln(x^n) = n ln(x)

Tim Mooney

Dear Loretta,

Algebra and logs are the keys to solving for n.

Given: T = P(1+r)^n

Solve for n

1.Divide both sides by P
T/P = (1+r)^n

2.Take the log of both sides (any log will do,
I like the natural log) ln (T/P) = ln [(1+r)^n]

3.When you take a log, one property is that any exponents of inside the log become coefficients of the log itself. ln (T/P) = n [ln (1+r)]

4.Divide both sides by [ln (1+r)]. [ln(T/P)]/[ln (1+r)] = n

This will give you a definitive answer for n, without guessing and checking.

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