# If tuition at a college is increasing by each year, how many years will it take 6.6% for tuition to double?

Jan 22, 2017

It will take $10.845 \ldots .$ years to double

#### Explanation:

Let current tuition rate be $t$

Then we need the condition $2 t$

Using the same model as for compound interest but setting final value after n years as $2 t$

$2 t = t {\left(1 + \frac{6.6}{100}\right)}^{n}$

Divide both sides by $t$

Note that $\text{ "1+6.6/100" " =" " 100/100+6.6/100" " =" } \frac{106.6}{100}$

$2 = {\left(\frac{106.6}{100}\right)}^{n}$

Taking logs of both sides

Note that $\log \left({a}^{n}\right)$ is the same as $n \log \left(a\right)$

$\log \left(2\right) = n \log \left(1.066\right)$

n=(log(2))/(log(1.066)

$n = 10.845 \ldots .$ years