Fidel O. answered • 12/17/20

I will help you learn the intuition behind Math.

Hello,

The continuous growth formula is A = Pe^{rt}

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 = Pe^{0.053t}

P is 1 so we can leave it out and just say 3 = e^{0.053t}

We take the natural log (ln) of both sides Ln(3) = Ln( e^{0.053t})

Now a property of math is Ln(e^{x}) is always equal to x

So Ln(e^{20}) = 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.