Question 1144914: The doubling time of an investment with continuous compound interest is 12.6 years. If the investment is worth $20,000 today, how much will it be worth 5 years from now?
It will be worth $_
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for continuous compounding is f = p * e ^ (r * n).
the doubling time is given as 12.6 years.
formula becomes 2 = 1 * e ^ (r * 12.6)
simplify to:
2 = e ^ (r * 12.6)
take the natural log of both sides of this equation to get:
ln(2) = ln(e ^ (r * 12.6))
by logarithmic rules, this becomes:
ln(2) = r * 12.6 * ln(e) which becomes ln(2) = r * 12.6
solve for r to get r = ln(2) / 12.6 = .055011681
confirm by replacing r in the original equaton with that to get:
2 = e ^ (.055011681 * 12.6)
e ^ (.055011681 * 12.6) = 2, confirming the continuous compounding interest rate is correct.
that interest rate remain the same, regardless of the number of years, so.....
f = 20,000 * e ^ (.055011681 * 5) = 26,332.15138.
that's your solution.
graphically, the continuoous compounding equation looks like this.
as you can see from the graph, the doubling time is every 12.6 years.
it went from 20,000 to 40,000 in 12.6 years and then to 80,000 in another 12.6 years.
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