Cover image credit: “Question” by kevin dooley is licensed under CC BY 2.0.

Here’s a curated selection¹ of the comments and questions shared by readers of this blog so far since the last Q&A post.

Q: How can you be financially sustainable without being financially independent?
A: Being financially sustainable (FS) means your total income – including both active and passive – are sufficient to meet your total expenses, whereas being financially independent (FI) means your passive income alone suffices for the same purpose. This implies that you can be FS while still needing to work a job, but being FI means you no longer need a job. In this sense, FS is a broader concept than FI.

C: I liked your explanation of how budgeting can be used as a tool for self-reflection – it is commonly portrayed only as a tool to rein in your personal finances.
R: Thank you – we believe that this “off-label” use of this tool can profoundly alter your lifestyle!

Q: You showed how to represent negative numbers on the number line, but how do we represent them on 2-D graph?
A: For a 2-D graph, you represent negative numbers on the X-axis in the same way as on the number line, i.e., to the left of the origin. For the Y-axis, positive numbers are traditionally marked above the origin, whereas negative numbers are marked below the origin as shown below.

Q: Your argument about using double-entry accounting is pretty convincing, but I’m unable to follow it as I’m unsure whether to enter a transaction as a debit or credit in a given account. How does one determine that?
A: Thanks for the clarification question. The general rule for credits and debits for accounts are: debits add to assets and reduce from liabilities, whereas credits do the opposite. Your assets are things you own, so in terms of accounts, it includes your bank accounts holding cash, e.g., savings accounts, cash on hand, etc. Similarly, liabilities are things you owe, so it includes things like your credit card balance. Thus, in terms of transactions, if a transaction adds to your bank account balance, it is a debit entry, if it reduces your balance, it’s a credit entry. Similarly, if a transaction increases your credit card balance, it’s a credit entry, whereas if it reduces your balance, it’s a debit entry. Hope this makes sense.

C: I am convinced that defeating mindless consumption is the biggest challenge of our generation. Maybe we can use the power of ads to undo the harmful effects unleashed by them in the first place.
R: That’s a great observation! Indeed, it’s in line with the old adage “fight fire with fire”, and certainly may be a very effective way of addressing this enormous challenge. The more ways we can come up with to defeating this challenge, the better.

Q: I liked your exposition of how solving equations can give you a reality check. Are there other ways that solving equations can clearly show if your plans are realistic?
A: Another way in which solving equations can help keep you honest with yourself is when you can actually solve for the quantity of interest, but the result is a negative number when you were expecting a positive number. As a simple example, say you want to know what your expenditure level should be if you desire to have annual savings of 75,000 LCU (local currency units) on an annual income of 25,000 LCU. From the fundamental budgeting equation, we can compute the annual expenditure level, $E$, in LCU as:

$$ \begin{equation} E = 25000 - 75000 = -50000 \end{equation} $$

But expenses cannot be negative, so you know that your plan is doomed to fail!

Q: You showed graphically how exponential growth exceeds linear growth, but what about when the interest rate is negative²?
A: Good question! For exponential decay, i.e., when the interest rate is negative, exponential decay can outpace linear decay. In other words, the total amount in the case of compound interest can be lower than that for the case for simple interest, as shown in the graph below with some example values.

Q: You mentioned that basic math can be used to compute the financial runway and how long it would take to create one of the desired length. How exactly can one do that?
A: We’re planning to release some supplementary material over the course of the next year to accompany the material in our blog posts, and will cover the details in that material – see the main website.

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