Interest

Interest is the reward for lending something to someone. In theory the interest could be anything, but in practice we are talking about money. The size of the interest is set by the interest rate together with a period of time, and it is worked out from the money you lent.

What is interest

Imagine that your rich Uncle Vic lends you £20,000. You can use this money however you like, but within a year you must pay Uncle Vic back £22,000, which is 10% more. If you don't manage it within a year, the amount owed will grow by another 10% every following year. This simple case lets us illustrate the basic terms:

• Uncle Vic is called the lender. The lender lends money and trusts that he will get it back.
• You have become the borrower. You owe money to Uncle Vic and you hope you will be able to repay it on time.
• The amount owed (or the principal) is the value of the money that the lender lent to the borrower. The amount owed can go down as well as up over time. In the story of Uncle Vic, it is the £20,000.
• The interest is the extra amount that Uncle Vic receives. If you manage to pay the money back within a year, the interest will be £2,000.
• The interest rate is usually a percentage that says how much the amount owed grows over time. Uncle Vic set a ten per cent interest rate.
• The compounding period tells us how often the interest is added. Often it is a year, but it can be shorter, for example a month or a quarter of a year. Uncle Vic was fairly kind and set the compounding period to one year.

How to work out interest

Most often you will want to work out the size of the interest and compare which loan (or, the other way round, which savings account) is best for you. What do you need for that? You need to know the amount owed, the interest rate and the compounding period. First let's work out the interest after one period (if the period is a year, after one year):

$$\text{interest}=\frac{\text{amount owed}\cdot \text{interest rate}}{100}$$

We write the interest rate as a percentage. This gives us the interest after one year, after one calculation. Let's try it for Uncle Vic. The amount owed is £20,000 and the interest rate is 10%.

$$\text{interest}=\frac{\text{amount owed}\cdot \text{interest rate}}{100}=\frac{\mathrm{20,000}\cdot 10}{100}=\mathrm{2,000}$$

This interest is usually added to the amount owed, and a year later, at the next calculation, the interest will be higher as a result. After a year you owe twenty thousand pounds plus a further two thousand (£22,000). The problem is that if you don't repay anything, next year the debt is worked out from this amount, not from the original £20,000. So for the second year the interest is:

$$\text{interest}=\frac{\text{amount owed}\cdot \text{interest rate}}{100}=\frac{\mathrm{22,000}\cdot 10}{100}=\mathrm{2,200}$$

So the amount owed has gone up, and so has the interest. After two years you owe Uncle Vic 22,000 + 2,200 = 24,200 pounds. The next interest is again worked out from this new, higher amount, so it will be a little higher still. This brings us to the idea of compound interest, which is the extra amount you pay after several compounding periods, that is, after several years in which more interest was added every year.

External links

• Interest on Wikipedia
• How to work out mortgage interest