SOLUTION: 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?

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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SOLUTION: 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?

SOLUTION: 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?