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Interest and compound interest

The interest for one year is the interest rate times the amount: 3% on 10 000 kr gives 0.03 · 10 000 = 300 kr. With compound interest, next year's interest is worked out on the new amount. After n years we have 10 000 · 1.03ⁿ kr.

Years 8–9 and upper secondary · Updated

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The interest for one year

Interest is the price of borrowing money. When we save, the bank pays interest to us. When we borrow, we pay interest. The interest rate is given in percent per year.

We want to know how much the interest is and how the amount grows.

interest = interest rate · amount

Compound interest: year by year

If the interest stays in the account, next year's interest is worked out on the bigger amount. So the interest grows every year.

YearAmount at the startInterest, 3%Amount at the end
110 000 kr300 kr10 300 kr
210 300 kr309 kr10 609 kr
310 609 kr318.27 kr10 927.27 kr

The formula with a change factor

After one year we have 100% + 3% = 103% of the amount, so the factor is 1.03. We write the same factor several times as a power.

10 000 · 1.03 · 1.03 · 1.03 = 10 000 · 1.03³ = 10 927.27

In general: amount after n years = starting amount · change factorⁿ. With 5% interest the factor is 1.05.

Example

Example 1: Saving for one year

Alva deposits 8 000 kr at 2.5% interest. We want to know the interest and the amount after one year.

  1. We write the interest rate as a decimal.

    2.5% = 0.025

  2. The interest is the interest rate times the amount.

    0.025 · 8 000 = 200

  3. The new amount is the deposit plus the interest.

    8 000 + 200 = 8 200

With a change factor: 8 000 · 1.025 = 8 200 kr. The same answer.

Example 2: Compound interest for three years

Leo saves 5 000 kr at 4% interest for three years. We want to know the amount after three years.

  1. The change factor for 4% is 1.04. After the first year:

    5 000 · 1.04 = 5 200

  2. In the second year, the interest is worked out on 5 200 kr.

    5 200 · 1.04 = 5 408

  3. In the third year, the interest is worked out on 5 408 kr.

    5 408 · 1.04 = 5 624.32

  4. All in one step with a power.

    5 000 · 1.04³ = 5 624.32

  5. After three years there is 5 624.32 kr in the account.

Without compound interest: 5 000 + 3 · 200 = 5 600 kr. The extra 24.32 kr is interest on earlier interest. That is reasonable.

Example 3: Interest on a loan

A loan of 30 000 kr has 6% interest. We want to know the interest before and after a repayment.

  1. The interest in the first year is 6% of the debt.

    0.06 · 30 000 = 1 800

  2. Per month, that is roughly the yearly interest divided by 12.

    1 800 ÷ 12 = 150

  3. We make a repayment, which means we pay off 10 000 kr. The debt is now 20 000 kr, and the interest is worked out on that.

    0.06 · 20 000 = 1 200

  4. In the second year the interest is 1 200 kr, which is 100 kr per month.

1 800 ÷ 30 000 = 0.06 and 1 200 ÷ 20 000 = 0.06. The interest is 6% of the debt in both years.

Pitfalls

  • Multiplying the first year's interest by the number of years, so that 5 000 kr at 4% for three years becomes 5 600 kr.

    Each year the interest is worked out on the new amount: 5 000 · 1.04³ = 5 624.32 kr.

  • Writing the change factor for 4% interest as 1.4 or 0.04.

    We keep the amount and add the interest: 1 + 0.04 = 1.04. The factor 1.4 means 40% interest.

  • Thinking that the yearly rate applies per month, so that 6% on 30 000 kr becomes 1 800 kr a month.

    1 800 kr is the interest for a whole year, so roughly 1 800 ÷ 12 = 150 kr per month.

Practise on your own

0 of 4 correct

  1. You save 2 000 kr at 3% interest per year. How much interest do you get after one year?

  2. A loan of 15 000 kr has 8% interest per year. How much interest is that per month, if we share the yearly interest equally over 12 months?

  3. You deposit 12 000 kr at 2% interest per year and leave the money for two years. How much is in the account then?

  4. You save 10 000 kr at 5% interest per year for three years, with compound interest. How much is in the account after three years?

More walkthroughs with Fox

Common questions

What is the difference between interest and compound interest?

Simple interest is worked out on the starting amount. With compound interest, the interest is added to the amount, so next year's interest is bigger.

How do you work out interest per month?

Work out the yearly interest and divide by 12. 6% on 30 000 kr is 1 800 kr per year, roughly 150 kr per month.

How long does it take to double your money?

Look for the n where the change factor to the power of n becomes 2. With 5%: 1.05¹⁴ ≈ 1.98 and 1.05¹⁵ ≈ 2.08, so roughly 15 years.

How do you write the change factor for an interest rate?

Add the interest rate in decimal form to 1: 3% gives 1.03 and 2.5% gives 1.025.

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