Question

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

Answer 1

It will take `10.845....` years to double

Explanation:

Let current tuition rate be `t`

Then we need the condition `2t`

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

`2t=t(1+6.6/100)^n`

Divide both sides by `t`

Note that `" "1+6.6/100" " =" " 100/100+6.6/100" " =" " 106.6/100`

`2=(106.6/100)^n`

Taking logs of both sides

Note that `log(a^n)` is the same as `nlog(a)`

`log(2)=nlog(1.066)`

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

`n=10.845....` years