The continuous growth formula is A = Pert
A is the final amount
P is the principal amount or starting point
r is your rate of growth [our 5.3 percent which is 5.3/100 = 0.053]
t is time
We are looking for time in this case.
Well we know what A is. It is three times the value of P. A = 3P The formula then changes to
3P = Pe0.053t
P is 1 so we can leave it out and just say 3 = e0.053t
We take the natural log (ln) of both sides Ln(3) = Ln( e0.053t)
Now a property of math is Ln(ex) is always equal to x
So Ln(e20) = 20 Take that to our formula and we get
Ln(3) = 0.053t Divide both sides by 0.053 to get our t. You can jut plug this into a calculator...
t = 20.728 or 21 years to triple your investment.