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

1 Answer
Dec 8, 2016

Answer:

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.