Question 239772
Formula for continuous compounding is:


FV = PA * e^(rt)


FV = future value
PA = present amount
e = scientific constant of 2.718281828.....
r = annual interest rate
t = time in years


In your equation,


FV = 2
PA = 1
e = 2.71828182818.....
r = r
t = 12


Equation becomes:


2 = 1 * e^(12r)


This becomes:


2 = e^(12r)


Take natural log of both sides (natural log is log to the base of e)


ln(2) = ln(e^(12r)


By laws of logarithms, this becomes:


ln(2) = 12r*ln(e)


ln(e) = 1


Equation becomes:


ln(2) = 12r


Divide both sides by 12 to get:


ln(2)/12 = r


Solve for r to get:


r = .057762265 * 100% = 5.7762265%


Using continuous compounding, an annual interest rate of 5.7762265% will double your money in 12 years.


Confirm by plugging into the original equation.


2 = 1 * e^(.057762265*12)


Simplify to get:


2 = 2 confirming the value of r is good.


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