l Rule of 72 at 6%
Enter Rule of 72 interest rate:
%

Answer
Success!
n ~ 12

↓Steps Explained:↓



Using the Rule of 72...

How long for money to double at 6%?

Rule of 72 Formulas Infographic:

Rule of 72 Formulas

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 = 6%

n  =  0.6931 * 0.06
  0.06 * Ln(1 + 0.06)

n  =  0.6931 * 0.06
  0.06 * Ln(1.06)

Now simplify the 2nd term

n  =  0.6931 * 0.06
  i * 0.058268908123976

n  =  0.6931 * 1.0297086719446
  i

n~  =  0.72
  i

Substitute i = 0.06 into the quotient

n~  =  0.72
  0.06

n ~ 12
This means at an interest rate of 6%, we double our money approximately every 12 periods of time.

Related Calculators:  Compound Interest Accumulated Balance  |  Approximations of Interest Rate  |  Effective Annual Yield Rate
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