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Compound interest

When the interest is added to the balance, next year's interest also applies to the earlier interest. That is why the amount does not increase by the same number of kroner every year. The initial amount $a$ is multiplied by the growth factor once per year, for $n$ years. The capital after $n$ years is $a\cdot b^n$ . The same model is used for fees and price growth at a fixed percentage.

K = a\cdot\left(1 + \frac{p}{100}\right)^n

capital after n years

b = 1.05

growth factor at 5% interest

Symbols

$K$	the amount after n years	kr
$n$	number of years
$p$	interest per year	%

Example

20 000 kr at 5% interest for 3 years: $20\,000\cdot 1.05^3 = 23\,152.50$ kr.

The interest for one year is 1000 kr. After three years the increase is greater than 3000 kr, because interest earns interest.

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Part of Mathematics 1T: Exponential models.