Question

If an account that earns interest compounded continuously takes 12 years to do in value, how long will it take to triple in value?

Answer 1

We first need the growth factor `g`, the number that we use to multiply the amount with every year.

Explanation:

Example: if the yearly interest is `5%` then the amount is multiplied by `(100%+5%)/(100%)=1,05` every year, so after three years it is multiplied three times, or by
`1.05xx1.05xx1.05=1.05^3=1.157625`

We need to find `g` from `g^12=2`
`g=root 12 2=2^(1/12)=1.05946...`

Next we need to solve `(1.05946...)^t=3` for `t` (in years).

Method 1 - Using logs:
`log (1.05946...)^t=log 3->`
`t*log 1.05946...=log 3->`
`t=(log 3)/(log 1.05946...)=19.02...->`

Answer : `t=19.02` years.

Method 2 - Using the GC:
Set `Y_1=1.05946^X`
Set `Y_2=3`
You may want to adjust your Windows setting to:
`X: 0 to 24` (twice the time for doubling)
`Y: 0 to 6` (so the horizontal line will be in the middle)
Now use the Intersect function.