Enter Rule of 72 interest rate:
%

Using the Rule of 72...

How long for money to double at 14%?

Doubling Time Definition:

(1 + i)n = 2

1 unit of money doubles in
n periods at interest rate i is:
(1 + i)n = 2

Take the natural log of both sides:

Ln(1 + i)n = Ln(2)

Use a logarithmic identity

Ln(an) = n * Ln(a)

Using that identity, we have a = (1 + i):

n * Ln(1 + i) = Ln(2)

Divide both sides by Ln(1 + i)

n  =  Ln(2)
  Ln(1 + i)

n  =  0.6931
  Ln(1 + i)

Multiply the top and bottom by i

n  =  0.6931 * i
  Ln(1 + i) * i

Plug in our interest rate of i = 14%

n  =  0.6931 * 0.14
  0.14 * Ln(1 + 0.14)

n  =  0.6931 * 0.14
  0.14 * Ln(1.14)

Now simplify the 2nd term

n  =  0.6931 * 0.14
  i * 0.1310282624064

n  =  0.6931 * 1.0684717741717
  i

n~  =  0.72
  i

Substitute i = 0.14 into the quotient

n~  =  0.72
  0.14

n = 5.1428571428571
This means at an interest rate of 14%, we double our money approximately every 5.1428571428571 periods of time.


You have 2 free calculationss remaining



What is the Answer?
n = 5.1428571428571
How does the Rule of 72 Calculator work?
Free Rule of 72 Calculator - Calculates how long it would take money to double (doubling time) using the rule of 72 interest approximation as well as showing the mathematical proof of the Rule of 72.
This calculator has 1 input.

What 3 formulas are used for the Rule of 72 Calculator?

Doubling Money Time (t) = 0.72/i
(1 + i)t = 2


For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Rule of 72 Calculator?

approximation
anything that is intentionally similar but not exactly equal to something else.
compound interest
the interest you earn on principal and interest
A = (1 + r/n)nt
interest rate
the proportion of a loan that is charged as interest to the borrower or proportion of principal credit given to a depositor
logarithm
the exponent or power to which a base must be raised to yield a given number
rule of 72
a simplified formula that calculates how long it will take for an investment to double in value, based on its rate of return.
t ~ 72/i
yield
How much an investment returns in terms of interest rate
Example calculations for the Rule of 72 Calculator
  1. Rule of 72 at 2%
  2. Rule of 72 at 3%
  3. Rule of 72 at 4%
  4. Rule of 72 at 5%
  5. Rule of 72 at 6%
  6. Rule of 72 at 7%
  7. Rule of 72 at 8%
  8. Rule of 72 at 9%
  9. Rule of 72 at 10%
  10. Rule of 72 at 11%
  11. Rule of 72 at 12%
  12. Rule of 72 at 13%
  13. Rule of 72 at 14%
  14. Rule of 72 at 15%
  15. Rule of 72 at 16%
  16. Rule of 72 at 17%
  17. Rule of 72 at 18%
  18. Rule of 72 at 19%
  19. Rule of 72 at 20%
  20. Rule of 72 at 21%
  21. Rule of 72 at 22%
  22. Rule of 72 at 23%
  23. Rule of 72 at 24%
  24. Rule of 72 at 25%
  25. Rule of 72 at 26%
  26. Rule of 72 at 27%
  27. Rule of 72 at 28%
  28. Rule of 72 at 29%
  29. Rule of 72 at 30%

Rule of 72 Calculator Video


Rule of 72 Infographic

Rule of 72

Tags:



Add This Calculator To Your Website




An Automated Online Math Tutor serving 8.1 million parents and students in 235 countries and territories.

Our Services

Top Categories

Community