Åk 6–9
4.4 Interest
When you loan money in Sweden, for example from a bank, you must pay interest.  If you save money you then receive interest.  Interest is then the price of loaning or loaning out money, and is usually a portion (percentage) of the amount loaned.  If you pay the same interest each year, we call it fixed interest, and we can calculate the interest by using the rate of change.

Loan Debt
A person has loaned 5,000 kr from a bank. He will pay 8 % interest every year.  He will pay the entire loan back after three years.

After one year the interest at 8 % of 5,000 kr costs:
0.08 · 5,000 kr = 400 kr.

The entire debt is then: 5,000 kr + 400 = 5,400 kr

Then you do the same calculation for each year.

You can also directly calculate the debt this way by using the rate of change:

The debt after 1 year:


The debt after 2 years:


The debt after 3 years:

This multiplication can also be written as a power:

1.083 · 5,000 kr = 6,299 kr

By using powers, you can calculte the total debt after n number of  years:
1.08n · 5,000 kr