Math Is Fun Forum

Eddie

Guest

"Rule of 70"

The “Rule of 70" is a rule of thumb to estimate how long it takes money in a bank to double.
Suppose the money is in an account earning i% annual interest, compounded yearly. The Rule
of 70 says that the time it takes the amount of money to double is approximately 70/i years,
assuming i is small. Find the local linearization of ln(1 + x), and use it to explain why this rule
works. 

Help please?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: "Rule of 70"

Hi Eddie;

Straight out of my notes which is straight out of wiki, I think.
First seen this analysis done by the great Abraham De Moivre on a combinatorics problem.

When the money doubles you have FV = 2PV so substitute,

Clean that up!

Just solve for t by taking the natural log of both sides.

When r is small then r is a good approximation of ln(1 + r) see the First term of the Taylor series, this is what you call a local linearizarion.

That is your rule of 70. It is nothing more than ln(2) which is .693... Very close to 70%.

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