Quantitative Interest Returns

Today, I learned about Benford’s law from Jacob.  If you read either of those links, you can see that if you apply Benford’s law to an exponential function you can find the probability distribution of the exponential function.  As Jacob’s post mentions, compounding interest is an exponential function.

After I compared time and interest rate dependencies in the exponential function, I started wondering more about relative interest return rates.  I believe applying Benford’s law now closes that loop.


The bar plot is the probability distribution of Benford’s law, and the line plot is the cumulative probability distribution of it.  Then, you can apply this to principal in a loan, fraction of a desired capital investment goal, and so forth.

Say you take out a loan, and pay 20% down.  The loan is free from 48% of the total interest compounding.  In other words, the loan is growing at 52% of the total loan potential, as a function of the lending interest rate.

It’s something to think about, and it’s also a tool to use if you apply time to calculations, like if you start to default on payments/investments.


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