An investor places $N,000 into a
stock fund. 10 years later the account has a value
of $M,000. Using logarithms and antilogarithms,
determine the average annual growth rate for this fund.
(Round to the nearest integer.)
If you start with N
and in 10 years you
get M
, then you want to solve
for X
in the equation N * X^{10} = M
.
You will need to use logs/antilogs. Fortunately, you can
use whatever base you want for the logarithm. Since many
scientific calculators will calculate the natural log
(base e
, called \ln
) and will also give
you e^x
, this might be the easiest base to work
with.
Solving for X
gives us:
X^{10} = M/N
10 \ln X = \ln M/N
\ln X = (\ln M/N)/10
X = e^{(\ln M/N)/10}
Find a calculator that can solve this for you.
If X
is a number like 1.123, then the annual
percentage increase is 12.3%, which to the nearest integer is 12%.