SOLUTION: An investment with an interest compounded continuously doubled itself in 12 years. What is the interest rate?
Algebra.Com
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.
RELATED QUESTIONS
An investment with interest compounded continuously doubled itself in 10 years. What is... (answered by josgarithmetic)
An investment with interest compounded continuously doubled itself in 16 yr. What is the... (answered by Theo)
An investment with interest compounded continuously doubled itself in 16yr. What is the... (answered by solver91311)
An investment of $20,000.00 will be doubled in 14 years with interest compounded... (answered by stanbon)
An investor with interest compounded continuously doubled in 15yr. What is the interest... (answered by edjones)
An investment with interest compounded continuously doubled itself in 16yr. What is the... (answered by Alan3354)
Solve. Where appropriate, include approximations to four decimal places.
An investment... (answered by rfer,MathTherapy)
what interest rate is required for an investment with continuously compounded interest to (answered by jim_thompson5910)
What rate of interest is required to triple an investment in 12 years if the interest is... (answered by lwsshak3)