How compound interest works

Compound interest is a fascinating thing. On one hand it means that your money can make more money. Its like you put the money in the ground and a money tree sprang up to give you lots of new money. On the other hand, it can mean that you can never pay off a debt you owe because as you are paying the debt, it continues to grow.

Lets assume you are on the good side of argument and you want to grow you money. How does compound interest work? To see this lets image we have $1 and an interest rate of 100%.

Beginning year 0, we have $1.

After 1 year, we have $2. For the mathematically inclined: 1*(1+interest rate) = 1*(1+1)=2.

After 2 years, we have $4. Again, 2*(1+interest rate) = 2*(1+1)=4.

After 3 years, we have $8. Here too, 4*(1+interest rate) = 4*(1+1)=8.

So what happened? After the first year the $1 we had produced one more dollar. But year 2 we have $2. So each of these dollars produced another dollar resulting in 4 dollars. Now in years 3, each of the four dollars produced one dollar so we ended up with 8 dollars. So essentially every dollar produces $1 per year.

Because the new dollars also continue to produce other dollars, the effect of adding money via old money compounds year after year. This is why this interest type is called compound interest. And it literally looks like this:

Of course in real life this doesn’t work out quite so nicely. Usually you are given a much lower interest rate. For example, historically the rate of inflation in the US has been around 3%. Lets say for shorthand that this means that savings accounts have averaged a savings rate of 3%. This means that each dollar in your savings will grow by about 3 cents per year.

Now you might wonder to yourself, well if I’m only getting 3 cents for each dollar saved then why is this even worth it? Well it is worth it because even though the proverbial snowball will roll slower, it will roll. There is a handy shortcut to figuring out exactly how long that snowball is going to take. This is called the rule of 72.

The rule of 72 tells us that 72 divided by the interest rate will tell you how many years it will take to double your money. So for example, with a 3 percent savings rate, your money will double in 24 years. Not bad, considering the fact that if you wanted to double your money without compound interest you would have to: A. work twice as much, B. rob the bank of mom and dad, or C. drink heavily until the world appears to double.

Furthermore, the inflation rate being positive actually means your money is worth less than it used to be every single second. So a 3% inflation rate tells us that prices will have doubled in 24 years, so having saved your money simply means you will be able to purchase the same amount of goods and services as you did 24 years ago. At this point you might be thinking about 10 cent shaves or 5 cent papers. If you savings and income had simply grown at the compound interest rate of 3%, then today we literally still live in the world of 10 cent shaves, just with bigger numbers.

Now that we’ve dwelled on the good side of compound interest. Lets briefly discuss the bad side of compound interest. Suppose you bought $100 of stuff on your credit card, at the ludicrous rate of 25% interest. Now suppose you pay $25 off each year. Lets repeat our chart:

Beginning year 0, we owe $100.

After 1 year, we owe $75 plus interest, which comes out to be $18.75. For the mathematically inclined: (100-25)*(1+interest rate) = 75*1.25=93.75.

After 2 years, we owe $68.75 plus interest, which now comes to 17.18. Again, (93.75-25)*(1+interest rate) = 2*(1.25)=85.94.

And this continues, in fact, it continues for over 8 years. Your total payments into the credit card are now $504. Amazing, you borrowed $100 and compound interest caused you to pay $504. And that, in summary in conclusion, is why one should always keep compound interest on their side.

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