Question 1198838: You are investing money at 10.5 percent annual interest, compounded continuously. It will take you ______ years to double your investment.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! continuous compounding formula is f = p * e ^ (r * t)
f is the future value
p is the present value
r is the interest rate per time period
t is the number of time periods.
in this problem, the time periods are in years.
formula becomes 2 = 1 * e ^ (.105 * t)
simplify to get 2 = e ^ (.105 * t)
take the natural log of both sides of the equation to get:
ln(2) = ln(e ^ (.105 * t))
by log rules, this becomes:
ln(2) = .105 * t * ln(e)
since ln(e) = 1, this becomes:
ln(2) = .105 * t
divide both sides of the equation by .105 to get:
ln(2) / .105 = t
solve for t to get:
t = 6.60140272.
confirm by replacing t in the original equation to solve for f, to get:
f = e ^ (.105 * 6.60140272) = 2.
this confirms the value of t is correct.
your solution is that it will take 6.60140272 years for you to double your investment.
this works for any amount of investment.
for example, if your investment is 500 dollars, then 500 * e ^ (.105 * 6.60140272) will get you 1000 dollars.
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