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Interest

Kapitoly: Interest, Compound interest, Gradual interest, How to calculate interest on a mortgage

Interest is a reward for lending something to someone. In theory, interest can be anything, but in practice we are talking about money. The amount of interest is specified by the interest rate along with the time interval and is calculated on the money you have lent.

What is interest

Imagine that your rich Uncle Vik lends you two million crowns. You can use the two million as much as you want, but you have to pay Uncle Vik back 2 200 000 kroner within a year, i.e. 10% more. If you don't make it within one year, the amount owed will increase by another 10% each year. Let's use this simple example to illustrate the basic concepts:

  • Uncle Vic is called a creditor. A lender lends money and believes he will get it back.
  • You have become the borrower. You owe money to Uncle Vik and hope you can pay it back on time.
  • The amount owed (or principal) is the value of the money the creditor has lent to the debtor. The amount owed can go down or up over time. In the story of Uncle Vik, it is the two million.
  • The interest is the extra amount Uncle Vik gets. If you manage to get the money within one year, the interest will be 200,000 kronor.
  • The interest rate (or interest rate) is usually a percentage of how much the amount owed increases over time. Uncle Vik set a ten percent interest rate.
  • The time period tells us how often the interest will increase. Often it is a year, but it can be less, for example a month or a quarter. Uncle Vik was quite kind and set the time period at one year.

How to calculate interest

Most often, you'll probably want to calculate the amount of interest and compare which loan (or, conversely, savings) is best for you. What will you need to do this? You need to know: the amount owed, the interest rate and the time period over which the interest is recalculated. First, calculate what the interest will be after one period of time (if it's a year, then after a year):

$$\mbox{ Credit }=\frac{\mbox{ amount due } \cdot \mbox{ interest rate }}{100}$$

We write the interest rate as a percentage. This tells us what the interest is after one year, after one recalculation. Let's do the math with Uncle Vic. The amount owed is two million, the interest rate is 10%.

$$\mbox{ Credit }=\frac{\mbox{ amount due }\cdot \mbox{ interest rate }}{100}=\frac{2{,}000,000\cdot10}{100}=200{,}000$$

This interest is usually added to the amount owed, and in one year's time, at the next recalculation, the interest will be that much higher. So after a year you owe two million and two hundred thousand on top of that (2,200,000). The problem is that if you don't pay anything back, the next year the debt will be calculated on that amount, not the original two million. So in two years you will have interest:

$$\mbox{ Credit }=\frac{\mbox{ amount due }\cdot \mbox{ interest rate }}{100}=\frac{2{,}200,000\cdot10}{100}=220{,}000$$

So the amount owed has increased, but so has the interest. After two years, you already owe Uncle Vik 2 200 000 + 220 000 = 2 420 000 crowns. The next interest will again be calculated on this new, higher amount and the interest will be slightly higher again. This brings us to the concept of compound interest, which is the extra amount you pay after several compoundings, i.e. after several years of additional interest being added each year.