The Mystery that is Compound Interest

In my article "Why we need to teach Personal Finance" I have already alluded to the damage compound interest can do. Especially, when no one seems to understand how it works, and how quickly it can spiral out of control. That's why I decided to write this article, so that hopefully we can gain some more insight, clear some confusion and take away some misconceptions about interest rates, and compound interest.

Most forms of debt come at a cost. This cost is often referred to as interest. Interest is the money you pay to whoever is lending you the money. You pay this for their service and, if the loan isn't secure (they can't take something away from you when you fail to pay) the interest can also reflect a security for the lender. Interest tends to be quite high in unsecured loans for this very reason.

However, it turns out many people don't understand how interest works. They don't understand how it works for debt, nor do they understand how it works for savings and investment. A one-off interest payment most people can wrap their head around, but when we start compounding, most people just tune out. But it's with compound interest that things finally start getting interesting...

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Compound Interest on Debt

I started outlining how compound interest works on my article on teaching personal finance again to children of primary and early high school age. The forms of debt I discussed there were mortgages, personal bank loans, credit card debt, peer loans and payday loans. It's the credit card and payday loans that make for the most interesting compound interest stories:

Payday loans Let's start with my "favourite": the payday loan. Where the shark lends money to the guppy. Think of men in shiny suits, with slicked-back hair, gold chains, gold rings and smoking skinny cigarettes who are trying to say "they will help you out."

And then think again. These type of malpractices (because that's what they are) have been taken over by actual businesses. I won't name names, but there is actual lending companies (although they often do get shut down) who are sharks praying on guppies.

Their advertisements may appear anywhere, promising you quick access to 400 pounds to tie you over at no risk to you. Just like a friend. But these deals are no friend to you. Let me explain how the debt and the compound interest works on these loans: You started out borrowing only a small sum of money (payday loans don't tend to be huge), so you think you should be relatively safe. Wrong. Even though we are only talking interest rates on small amounts of money, the rate of interest is really high. And needs to often be paid daily or weekly rather than monthly or yearly. And that's where they get you. Imagine this scenario: you took out $500 to be repaid in 5 weeks, against 10% per day (I imagine that rate is somewhere hidden in the small print). Day 1 is $50 in interest, and so are days 2-7. On day 7 you also repay the first instalment, which is another $100. In total, week 1 has cost you $100 in repayment + $350 in interest, totalling $450. Within week 1 alone, you have almost paid the entire sum you borrowed, most of it not being in repayment, but in interest rates.

Given that we still have 4 weeks to go, you'll end up paying so much more than the initial sum. This is the damage compound interest can do. Especially if it's charged per day...

Credit card debt Now not everyone falls into the trap of the payday loan. Lots of people do see through them or have been warned against them (you have been warned now). But something that very often isn't warned against, no, is even widely accepted, is the credit card. Having this type of consumer debt has almost been completely normalised. So let's look deeper into this one.

Credit cards are incredibly convenient. You can spend money now, that you don't have now but are likely to have later. Often, people pay off their credit card bills at the end of the month, or the beginning of the month, whenever their wage comes in. However, sometimes people don't pay their debt off at all. Imagine you don't pay off your credit card debt. Imagine that you have taken $5000 out on it, and your credit card has an APR (Annual Percentage Rate, just means interest), of 23%. Yes, that is high, but that's a standard rate. You will face a 23% charge on the 5000 every year, because it's calculated annually. However, interest payments can still come every month. You can just take 1/12th of 23%, which is about 2% (for ease). If you keep on this loan for a full year, that's 1150 in interest. Not in repayment, just in interest. On a monthly basis, you pay 0.02 x 5000 which is "only" 100 a month, for the pleasure of being in debt. It's up to you to decide whether that's worth it. If you do pay back your credit card debt, good for you! If you pay it back in full every month, you won't be charged at all. However, the majority of people don't pay back the full amount, they either pay back a percentage of their debt, say 10% (so in this example you'd pay back $500) or they only pay back the minimum payment. The minimum payment is a very low percentage, but it ensures that you are aware of the credit card debt and are able to pay it off. It's what keeps your credit card from being delinquent. However, this is quite a costly habit.

If you only pay back the minimum payment, which on a 5000 debt would be about $20, it's going to take a long time to pay down that debt. And every month, the monthly part of the APR will continue to be charged. In the first year your repayment will total 12 x 20, which is 240. That's not even 5% of the total debt. And don't forget the fact that you are still making interest payments! The first interest payment will be (5000-20) x 0.02, the second will be (4980 - 20) x 0.02 etc. It will still come quite close to having to pay 1000 over one year, to be able to borrow 5000. Don't believe me? Google it! There are plenty of examples that explain why minimum repayments are a bad idea: "Anybody with a credit card balance knows that making only the minimum payments takes a lot of your money but gets you nowhere. If you had a $5,000 balance on a card with an 18.9% interest rate and your minimum payment was $200 each month, it would take you 11 years and five months to pay the entire balance." This example came from Investopedia. Repaying your debt in over 11 years is a long time. And paying interest on that debt for over 11 years makes it an even longer time (you know what I mean).

Now some banks and credit card institutions might trick you with having the first half year interest free, but then the normal rate just kicks in half a year late. And it will still be expensive. So do keep that in mind!

Compound Interest on Savings and Investment

It isn't all bad though. I originally wanted to call this article "The Evil that is Compound Interest." But that's just not fair. Because compound interest can also be used for good. And it is one of the biggest arguments as to why you should start saving and investing early. Preferably yesterday.

Savings

Ok I'm going to keep this section short, because quite frankly, the interest on a savings account (the money the bank pays you for letting them keep your money (and the ability to lend it out to others...)) is currently incredibly low. But let's imagine better times, in which a savings account could yield you 2% per month.

Say you have $1000 in savings in year 1. Now, per month you get 2% interest on that. Most people make the mistake of doing 1000 x (0.02 x 12), which comes to 240. This is just calculating the interest, if you want the total you just add the 1000 to that. But that's not how compound interest works. In month one you get 0.02 of 1000 which is 20, but in month 2 you get 0.02 of 1020 etc. In the end you have 1000 x (1.02)^12, which ends up being 1268,24. Now you might be thinking, that the difference between 268,24 and 240 isn't particularly big, but this is calculated on a one-time deposit of 1000. If you were to do this every year for 40 years, there would be quite a hefty difference... Even leaving 1000 in a savings account for 40 years without adding any more payments to it would result in 1000 x (1.02)^480, which equals to 13.430,20. Not bad for a starting point of 1000! It's difficult to see where 2% of interest can take you, but if you leave it for long enough, money will grow. Now, I do have to mention this again: saving accounts hardly yield anything these days (you're lucky if they pay 0.5% annually), and with the rate of inflation being 2% per year, to save money for the longer-term is to reduce its value (but please do same for a rainy day fund and shorter-term goals!!!). As such, when looking at the longer-term, most people put their money away in investments, particularly the stockmarket. So let's see how that works with compound interest:

Investment Investing can be risky business, but unlike saving, it isn't a certainty that your money will lose value (when comparting savings rate to inflation rate).

Many people have made many claims about how well the market performs. Some say they can get annual returns of 10%, others roll their eyes and claim the market hadn't performed better than 6% to begin with. Whichever percentage you take (and yes, 10% is quite optimistic), they beat savings rates by quite a bit.

So let's say the average annual return of the stock market is somewhere in the middle, 8%. If you've invested 1000 about 10 years ago. You haven't added to it at all, neither have you taken away from it. Your stocks would now be worth 1000 x 1.08^10, which is 2158,93. Of course, if you had invested 2000 about 10 years ago, your stocks would now be worth 2000 x 1.08^10, which is 4317.85. So the more you invest, the better your money will grow. Now of course, no one said you had to only invest once. Some people top up their investments annually as well. Say you topped up your investments with 1000 every year, starting with an initial sum of investment of 2000 which you made 10 years ago. The calculation would look somewhat longer, but here's the gist of it: 2000 x 1.08^10 + 1000 x 1.08^9 + 1000 x 1.08^8 + 1000 x 1.08^7 + 1000 x 1.08^6 + 1000 x 1.08^5 + 1000 x 1.08^4 + 1000 x 1.08^3 + 1000 x 1.08^2 + 1000 x 1.08 = 4317.85 + 1999.00 + 1850.93 + 1713.82 + 1586.87 + 1469.32 + 1360.49 + 1259.71 + 1166.40 + 1080 = 17,804.39

That's a whole lot of money for you!

Now, some tales of caution here: The type of investment I'm describing here is investing in index funds. These funds tend to hold the whole market. You can invest in individual stocks or certain type of portfolios (the most notable being the vice portfolios made up of tobacco, alcohol and weaponry stocks). But, to do so successfully is to know that market

Another issue with the stockmarket is that you really should do it only for longer terms, and you need to have a bit of luck when it comes to timing when you get in and when you get out. Don't invest when the market is in a peak (or a boom, bubble or bull state) and don't sell when the market is in a dip (crisis, or bear state). For the rest, if you aim to stay in for the long haul, there's money to be made. But things like crashes do happen. Which is why you should only invest money you actually have (and not money from loans or credit card debt) and you should get advice if you don't really know what you're doing all that well!

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So, there you have it. Compound interest explained in terms of both debt and gains. There's money to be lost and there's money to be made. Just make sure that you fully understand what you are getting yourself into.

And when in doubt, get the calculator out!