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Compound interest

If you deposit an amount at a fixed annual rate, the amount is multiplied by the same growth factor every year. The interest one year is added to the balance and itself earns interest the next year. That is compound interest. The growth factor is 1 plus the rate as a decimal, and the exponent is the number of years. The formula applies when you deposit or withdraw nothing along the way. Fees are not included, so this is not the effective rate.

Kn=K0⋅(1+p100)nK_n = K_0 \cdot \left(1 + \frac{p}{100}\right)^nbalance after n years

Symbols

K0K_0the depositNOK
ppannual interest%
nnnumber of years

Example

10,000 NOK at 3% interest for 5 years: 10 000⋅1.035≈11 592.7410\,000 \cdot 1.03^5 \approx 11\,592.74 NOK.

5,000 NOK at 2% interest for 3 years: 5 000⋅1.023=5 306.045\,000 \cdot 1.02^3 = 5\,306.04 NOK.

The exponent is the number of years. The factor is 1 plus the rate, not the rate alone.
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Part of Mathematics 1P: Personal finance.