
profit question
A company made $100,000 profit this year. If they anticipate that profits will increase by 6% a year going forward, how long will it take for the profits to double?
A. Between 9 and 10 years
B. Between 10 and 11 years
C. Between 11 and 12 years
D. Between 12 and 13 years
E. None of the above
I was able to solve the question using excel
just wondering if there was some kind of equation in the case excel couldnt be used

This is a geometric progression, where the first term is 100 000, the second is 100 000(106/100) = 106 000, the thirs term 106 000(106/100) etc.
It can be resumed as:
$\displaystyle P_n = 100 000 (\frac{106}{100})^n$
For the profit to double, you should have at least 200 000.
$\displaystyle 200 000 = 100 000(\frac{106}{100})^n$
Solving for n,
$\displaystyle 2 = (1.06)^n$
$\displaystyle ln(2) = n ln(1.06)$
$\displaystyle n = 11.9$