But one of the things you quickly realize when learning about finances is that the amount of money you are worth--even if that figure is in the negative--is relatively unimportant. What is important is the delta--the change--in your net worth from time A to time B. Thus, from an investing perspective, there is no meaningful difference between investing in a stock that rises 15% and paying off a debt at a 15% interest. In both cases, you are netting a (very healthy) 15% return on your allocation of money. In fact, repaying the debt is by far the "better investment", because--unlike the risky gamble on the stock--its returns are guaranteed.
One particularly neat application of this sort of thinking is compound debt repayment, which harnesses the awesome exponential growth powers of compounding to pay off debts much faster than you might have realized--for free. Let me explain what I mean.
Suppose you take out a $10,000 loan at an interest of 10% per year, i.e. 0.83% per month. The interest is calculated every month, which means that every month you get charged 0.83% on the total amount that you owe. Supposing that you choose to allocate $150/month towards this debt, this is what your payment plan looks like*:
As you can see, in the first month we were charged $83.32 in interest bringing our total debt to $10,083.32--and then we paid it down by $150 to $9933.32. At this rate of $150/month, the debt is paid off in a little more than eight years.
However, a crucial thing to notice is that, though we may think we are being consistent in paying $150 every month towards the debt, in actuality we are allocating a smaller and smaller proportion of our income towards the debt each month. To see this, take a look at the amount of interest charged with each payment. Because the total amount owed decreases every month, the amount of interest charged also decreases every month. This is the same as additional income. So for example, in the second month we are charged $0.55 less for interest, which means that if we paid $150 towards the debt, then we would have an extra 55 cents rattling around in our pockets as compared to last month (remember, it is the delta that matters). Now, you could use that extra money towards food or a coffee or a movie rental--but you could also turn right around and use that money to pay off the debt. If you did this, instead of getting a 55 cent boost of income in the second month, your income would appear to remain the same as the first month.
A modest 0.55 cents might seem like it wouldn't make a significant difference, but it does--over time. If you were to continue to rollover the "income" provided by the decrease in interest every month, the debt would be paid off not in eight years, but in six:
(Click to enlarge.)
The paltry increase of $0.55 on the second payment turns into a mighty increase of $80 by the last payment. And if you can supplement that monthly increase in the nominal payment towards the debt--for example by redirecting money allocated on eating out, only if it's just one meal a month that is sacrificed--then you will shave even more time off of your debt repayment.
Now, if you read this twice and said, "Wait a minute, this is bullshit--you don't have an extra $0.55 rattling around in your pocket at all", then there is something that needs to be clarified about what a loan is. For some reason we have a whole lot of separate jargon when it comes to money that obscures a crucial insight about it, which is that it is no different than any other product out there in the market. It is no different, for example, than a DVD--there is demand for it, some companies supply it, and when demander and supplier agree on a price, the transaction goes down. In precisely the same way that you can rent a DVD by going to Blockbuster and paying a small fee for the privilege of taking out a copy of Coyote Ugly and returning it by a certain due date, you can go to a bank and pay a small fee for the privilege of taking out some dollar bills and returning them by a certain due date. The only difference is the jargon: for DVDs we say "rent" and with money we say "borrow", and with DVDs we say you pay "a rental fee" whereas with money we say you pay "interest".
So keeping this in mind, it is important to keep track in your ledger the distinction between what you are renting from the bank (the ten thousand dollar bills), and the fee the bank is charging you for the rental. In fact, what causes a whole lot of confusion is the fact that it just so happens that what you are renting from the bank is kept in bank accounts along with your real money--making it look like the rented dollar bills are a part of your whole system of income and allocation, when in fact they are not. They are better thought of as objects, like DVDs, that you rent and keep around the house and have to return at a later date. What is a part of your system of income and allocation, however, is interest, since this is similar to the $2 fee you pay to Blockbuster to rent the DVD (and certainly, like DVD rental fees, money rental fees are something you want to track as an expense).
With all this straightened out, we can see why it makes sense to say you have "an extra $0.55" rattling around in your pocket in the second month of repayment. The actual expense of borrowing--or renting--the ten thousand dollar bills is the interest payment. When you "pay down" the principle, what you are really doing is returning some of the bills that you had rented out. Of course, since you're renting out less bills, you will be charged less in rental fees. What compound repayment of debt says is: hey, now that you're paying less in money rental fees, you don't need to have as many dollar bills rented out! Return those bills, it's expensive to keep them rented out so long!
*These calculations are rough estimates. In the first place, the numbers were clumsily rounded before being displayed (don't worry--the numbers computed internally were not rounded), so some of the arithmetic shown might not be consistent to the penny. Second, there might be some float point inaccuracies. But I don't think the numbers are big enough that this would make a huge difference. Long story short: I hastily slapped this together to demonstrate a point in a blog post, so take it with many grains of salt.
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