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 couldn't be used

The equation to use to find the number of periods to double your investment is:


(1+i)^n = 2


Which you can rearrange and solve for n by taking the logarithm of both sides of the equation:


n = \frac {log 2} {log(1+i)}


There's an easier way however, if an estimate is good enough. A handy rule-of-thumb that you can use is called "the rule of 72." Divide 72 by the interest rate and you get a pretty good estimate of how long it takes an investment to double. So here you'd have 72/6 = 12 years. It's not exact, but it works pretty well for "reasonable" values of i.