Einstein once said, **Compound interest** is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it. **Compound interest** is the most powerful force in the universe.

Everyone likes the thought of earning interest on their savings and investments (check out how to invest to start investing), but you are also charged interest on loans, credit cards, and other debts, this is how the loan companies make money, and lots of it.

### Compound interest, what is it, and why is it so important?

Here is an explanation that should make everything quite clear. Lets say you take out a loan of £1000 over 1 year, and it has 10% interest on it calculated out over 1 year, you will have to repay £1100, as 10% of 1000 is 100, so 100+1000 = 1100.

But, lets say you take out a loan over 5 years, the interest for the first year is calculated the same way, 10% of the initial borrowed figure, but, then the interest for the next period is calculated from the previous total.

That may not make any sense at all, it doesn’t really to me either… look at this example

Borrow: £2000 over 5 years

10% interest

Pay off £10 per month = £100 per year

Interest is £200 per year

End of the year, you will have paid off £100, leaving £2100. Now, the interest is calculated on £2100, not the initial figure of £2000.

**Example 2**

Let’s say you borrow £2,000 over a 3 year period, pay 10% annual interest on your debt and **are not making regular repayments**. In this case, the amount you will have to repay will look like this:

**Year 1**: £2,000 x 10% = £200.

**Year 2**: £2,200 x 10% = £220.

**Year 3**: £2,420 x 10% = £242.

The total repayment figure after 3 years is £2,662 (the £662 interest is the sum of each year’s interest).

It should be noted that if you make regular repayments on your loan, the total compound interest will be lower because the remaining principal on the loan will be decreasing at each compound interval.

### Why Compound Interest is Great for us Investors

As you can see from the example above, compound interest is great for those who give the money, but not for those who borrow it, so, if you invested £1000 over 20 year period, with an interest rate of 10%, you will have a great return, thanks to compound interest. Take a look at the graph below.

It would work something like this

**Year 1: **£1000 – Year Interest = £100

**Year 2: **£1100 – Year Interest = £110

**Year 3: **£1210 – Year Interest = £121

**Year 4: **£1331 – Year Interest = £133.10

**Year 5: **£1464.10 – Year Interest = £146.41

Each year, the previous years interest is added onto the total, and the next years interest is calculated on the updated figure. So, for us investors, I hope you can see why compound interest is so important.

### The Formula for Compound Interest

**M = P( 1 + i ) ^{n}**

**M** is the final amount you repay at the end of the loan.

**P** is the principal amount you borrow.

**i** is the annual rate of interest.

**n** is the number of years you borrow/invest over.

If we use the example of our £2,000 borrowed at 10% over 3 years (without repayments) we get the following calculation:

**M=2000(1+0.1) ^{3} = £2,662**