Jon P. answered • 05/08/15

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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.