Essentially, passive income is earnings where your efforts are not actively needed.  It is much easier to define active income: a job (where time and skill and traded for $bling).  In financial terms, passive income is generally investment capital traded for $bling.  Examples of passive income are dividends, apartment rent (if you own an apartment complex), and the part of the pyramid scheme where you profit from others’ efforts.

Passive income can also be viewed as potential.  As ERE’s post describes, the 25 and 33 scalars, applied to one’s annual budget, are commonly used for estimating this potential.

If you need your money to last 30 years and you invest it 100% in index funds and you withdraw your annual expenses every year, you need 25 times as much money in index funds as your annual expenses (including taxes).

If you need your money to last 60 years instead and follow the same procedure, you need 33 times as much money.

(If I remember correctly) this concept of potential is defined in Work Less, Live More.  The book, as well as firecalc, describe how those numbers take into account risk, so that one will be financially independent.

The time to generate these amounts are below,

in general terms, and

in a more applied form.

Applying the equation above in terms of the percentage of your pay that you save, you’ll come up with a pretty graph.  I have two versions, out of respect for the scale.  The first is in a scale for Joe American.  The second is for the whacky nut job ladies that plan to leave millions of dollars to their cats.

It’s interesting to see that saving extremely, in terms of one’s earnings, provides a nearly inversely proportional relationship in time for retirement.  These are not revolutionary ideas.  I just like visualizing numbers.

It’s interesting to note that spending less, as opposed to making more, has a greater impact to achieving financial independence, faster.  This is logical, if you look back to the equation.  The accumulation denominator is a function of earning and spending, yet the state of the system in the numerator is a function of spending scaled by a factor of 25.

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.

My current favorite online response is from blogcadre:

. . .
• The hands are nearly symmetrically balanced on [the] face of the dial at 10:08.  The minute hand is 48 degrees right of vertical, while the hour hand is 56 degrees left of vertical.  Exact symmetry would be achieved at 120/13 minutes past 10:00, approximately 10:08:13.8.  Other symmetrical times would not meet the needs above.

. . .

I cut out a lot of the real reasoning: marketing!

My thoughts centered around the symmetry, pun intended.  Namely, 10:08:13.8 is NOT symmetrical!  Amateurs. The second hand is messing up everything that is good in the world.  It’s all or nothing, man.

I thought about this visually, for both the second hand being between the two hands, if you will, and for the second hand being outside the other two hands.

Then, I came up with some killer balances.

Acute:   

Obtuse: 

For the joy of all, I solved those killer formulas. And, I provide you with a nice time table:

Now, you understand what I think of if you hear me say, “Yes, I strive to recognize balance in my life.”

Exploding with social popularity, Facebook always lets me know when my friends’ birthdays are.  Every few days I have a friend with a birthday, and that person’s received comments greatly increase that day.

Then my curiosity wandered: how many friends do I need to have in order to add a daily task of wishing someone a happy birthday? I used the lazy man’s approach: I avoided theory and just simulated. I used a uniform distribution for birthday odds. I continued the simulation until all of the 365 days were full, which I repeated a thousand times.

The upshot of this: you need 1900 to 2800 friends before you can feel any confidence that you can add the daily task of “wishing happy birthdays” in your virtual community.

Maybe by the time I have that many friends I’ll know a more elegant theoretical solution.