Question:
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?

Replies:
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.

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.