Question 239772: An investment with an interest compounded continuously doubled itself in 12 years. What is the interest rate?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
You might try some of the LESSONS FROM ALGEBRA.COM if you have the time. There's a few in the financial area that might help you.
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