how does compound interest work.

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how does compound interest work.

In: Economics

Compound interest means that the interest is added to the balance, and next period’s interest is calculated off of the total balance, including the interest. Hence, it compounds.

\$100 gaining 10% interest, compounding annually, grows like this:

End of year 1 – 10% of \$100 which is \$10, total balance is \$110.

End of year 2 – 10% of \$110 which is \$11, total balance is \$121.

End of year 3 – 10% of \$121 which is \$12.12, total balance is \$133.12.

End of year 4 – 10% of \$133.12 which is \$13.31, total balance is \$146.43

You see how each year the amount of interest goes up? It’s compounding – you’re getting interest on the interest.

Its really pretty simple. You have a certain amount of money – known as the princple – and interest is calculated at a fixed rate over a fixed period of time (known as the compounding period). The interest payment is then added to the original principle, and this higher amount becomes the _new_ principle for future calculations.

So, in an example. I have \$100 in principle that earns 10% interest every month, and it compounds monthly.

In month 0, I have \$100 (my original deposit)

At the end of month 1, I get \$10 in interest (\$100 * 10%) and its added to my original \$100, so now I have \$110

At the end of month 2, I get \$11 in interest (\$110 * 10%) and its added to my previous \$110, so now I have \$121

At the end of month 3, I get \$12.10 in interest (\$121 * 10%) and it is added to my previous \$121, so now I have \$133.10

Etc.

You have \$100 that you deposit the bank at 5% interest. At the end of the month, the bank pays you \$5 in interest. You now have \$105.

If you leave the \$105 in the bank for another month, you’ll earn more interest because you have more money. So instead of \$5 in interest, you’ll get \$5.25

Next month you’ll get another \$5.76, and the interest keeps going up.

I have \$10. I invest \$10 in an investment that will get me \$11 back every month, or a 1% return.

However, if I just keep that \$10 in the same investment I will get way more than that 1% return over time if I take the profits from the investment and invest that as well.

The first month I invest \$10, I get back \$11 for a profit of \$1

The second month I invest \$11 and get back \$12.1 for a profit of \$1.1

The third month I invest \$12.1 and get back 13.31 for a profit of \$1.21

Fast forward 10 years, and that \$10 has become \$27.07.

You earn interest on the initial amount, but also on the previous period’s interest.

say you have \$100 that gets 10% interest annually. At end of the year, you have \$110 — \$100+\$10 interest. The next year, you’d earn the 10% on that \$110, not just on the initial \$100, so you earn \$11 in interest.While it’s just a little difference early on, as the years go it, it starts to get much larger.

Compound interest is when you include the interest earned to the principle (initial money put in) when calculating future interest.

It’s a bit easier to understand with an example: say you put \$100 in a bank account earning 20% interest, annually. After your first year you would have \$120 (\$100 x 1.2). Assuming you don’t take or add any money, after your second year you would then have \$144 (\$120 x 1.2)

ELI3: Let me hold some money for a while and you will get extra, then later extra **of the extra too**!

ELI5: Simple interest = a bit of what you gave me. Compound interest = a bit of what you gave me and a bit of that bit. For example: Let’s use 10% a month interest. Let me hold your \$10 (so I can use it) and a month later if you want it back I’ll give you \$11. If I get to hold it another month it’ll go up not by \$1 to \$12 but by even more! If you want it back then you can get \$12.10. After 1 year you’ll have \$31.38. The magic really increases over time, so that in 10 years you’ll have **\$927,090.69**!

The interest you gain are added each period thus the calculation (ex : 5% of x\$ gets added to x\$ for the next periods 5%) becomes exponential the more period you add.

A cool math story I remember was if I give you \$1 on the first day of the month, then \$2 on the 2nd day, \$4 on the third, \$8 on the 4th, and I keep doubling that for 30 days, on the 30th day I’ll give you \$1,073,741,824

Let’s look at both simple and compound interest.

Simple: the increase in percent is relative to the initial amount. So the interest added will always the same amount.

While in compound the interest is a percent of the the initial amount + the interest added so far. So the new intrest added is always increasing!

It’s important to realize that compounding interest can work against you just as easily…

All these examples are “You invest \$100… you make \$110” and so on.

Compounding interest is also what makes paying debt, specifically credit cards (18%), mortgages (~3-4%),and student loans) so difficult. Imagine you borrow \$100, and pay back a share of it. But now, the \$100 you borrowed is actually \$118. And the next year it’s up to \$139. If you didn’t pay back a substantial amount, the interest is going to be more than you pay back. And then next month/year, all you’re able to do is cover the interest.

A real life example – if you get a mortgage over 25 years, you’re paying MOSTLY interest for the first 10-12 years of your payments. Your principal (the amount you borrowed) is barely affected because the interest is so high (based on a 25 year payment plan). If you borrow, \$500,000 – the compounding 3% interest will make that closer to \$750,000 by the time you pay it off.

You get interests on the interests you made.

For example :

You place 100\$ in an account at a really good rate of 100%. By the end of the year your account should have 200\$ in it, meaning you made 100\$ interests.

The thing is, your account is now 200\$, not 100\$ anymore. So if you keep this account at 100% for another year, your new balance at the end of year 2 will not be 300\$ (100\$ interests) but 400\$!! Because 100% of 200\$ is 200\$.

That means, during year 2 you made 2 seperate types of gains :

1) 100\$ on what you invested (wich is called interest)
2) 100\$ on your gains/interests of year 1(wich is called compound interest)

Compound interest on your personnal investments work the exact same way on smaller interests rates.