Rule of 72 at 13% ·

17 Jul 2024, 00:00

Rule of 72 at 13% Image to Crop

Using the Rule of 72...

How long for money to double at 13%?

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 = 13%

n =	0.6931 * 0.13
	0.13 * Ln(1 + 0.13)

n =	0.6931 * 0.13
	0.13 * Ln(1.13)

Now simplify the 2nd term

n =	0.6931 * 0.13
	i * 0.12221763272425

n =	0.6931 * 1.0636763051475
	i

n~ =	0.72
	i

Substitute i = 0.13 into the quotient

n~ =	0.72
	0.13

n = 5.5384615384615
This means at an interest rate of 13%, we double our money approximately every 5.5384615384615 periods of time.

You have 1 free calculations remaining

What is the Answer?

n = 5.5384615384615

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?

approximationanything that is intentionally similar but not exactly equal to something else.compound interestthe interest you earn on principal and interest
A = (1 + r/n)ntinterest ratethe proportion of a loan that is charged as interest to the borrower or proportion of principal credit given to a depositorlogarithmthe exponent or power to which a base must be raised to yield a given numberrule of 72a simplified formula that calculates how long it will take for an investment to double in value, based on its rate of return.
t ~ 72/iyieldHow much an investment returns in terms of interest rate

Rule of 72 at 13%

Using the Rule of 72... How long for money to double at 13%? (1 + i)n = 2 1 unit of money doubles inn periods at interest rate i is:(1 + i)n = 2 Ln(1 + i)n = Ln(2) Ln(an) = n * Ln(a) Using that identity, we have a = (1 + i):