how long does it take for an investment to double if it has an annual interest rate of 6.4% compounded continuously?

Answer 1

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 6.4 percent which is 6.4/100 = 0.064]

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.

Therefore, A = 2P The formula then changes to

2P = Pe^0.064t

P is 1 so we can leave it out and just say 2 = e^0.064t

We take the natural log (ln) of both sides Ln(2) = Ln( e^0.053t)

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

So Ln(e²⁰) = 20 Take that to our formula and we get

Ln(2) = 0.064t Divide both sides by 0.053 to get our t. You can jut plug this into a calculator...

t = 10.8 or 11 years to double your investment.