How long would it take to double your principle at an annual interest rate of 8% compounded continuously ?

Question

I just really don't understand how to do this.

Answer 1

The formula for continuous compounding is

 

A = Pe^rt

 

where

P = the starting amount

r = the interest rate as a decimal

t = the time

e = the number e

A = the amount you have after time t

 

Since they're not giving you a particular starting amount, you have to adjust the formula a little.

 

 

You're trying to double the starting amount.  That means that after time t, you want A to equal 2P.  So put that in the formula:

 

2P = Pe^rt

2 = e^rt

 

Also, r = 8% = 0.08, so you have:

 

2 = e^{0.08 t}

 

Take the natural logarithm of both sides:

 

ln 2 = ln (e^{0.08 t}) = 0.08 t

(ln 2) / 0.08 = t

8.66 = t  (approximately)

 

Since the interest was expressed as an annual rate, t is in units of years.  So the answer is 8.66 years.