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What you will learn
- Follow the base used for each year’s interest.
- Compare withdrawn interest with interest that stays in the account.
- Check a compound calculation without treating it as a forecast.
What happens to the first year’s interest?
Both accounts earn SEK 500 in the first year: 10,000 × 0.05. In account Keep, the interest stays in the account, bringing its value to SEK 10,500. In year two, 5% is calculated on that larger amount, producing SEK 525 in interest. The value becomes SEK 11,025. Year three adds SEK 551.25 and ends at SEK 11,576.25.
In account Withdraw, we move each year’s SEK 500 into a separate box that earns no interest at all. The account therefore begins each new year at SEK 10,000. After three years the box contains SEK 1,500 and the account contains SEK 10,000. Our comparison includes both parts, rather than counting only what remains in the account.
If the table does not fit, scroll it sideways.
| Time | Account Keep | Withdraw: account + interest-free box |
|---|---|---|
| Start | SEK 10,000 | SEK 10,000 + 0 |
| After year 1 | SEK 10,500 | SEK 10,000 + 500 |
| After year 2 | SEK 11,025 | SEK 10,000 + 1,000 |
| After year 3 | SEK 11,576.25 | SEK 10,000 + 1,500 |
Multiply by another factor for each year
For account Keep, write 10,000 × 1.05 × 1.05 × 1.05. The shorter notation is 10,000 × 1.05³. Compared with account Withdraw’s combined SEK 11,500, the difference is SEK 76.25. It comes from interest on earlier interest; the original deposit and annual percentage rate are equal in both accounts.
With the same annual rate r for n full years, the factor is (1 + r)ⁿ, with 5% written as 0.05. Our formula assumes interest is added once a year and stays in the account. Monthly deposits or a different interest period need a calculation that follows those particular dates and intervals.
Separate the model’s steady interest from changing values
A share does not automatically pay the model’s fixed interest rate. If a value first rises by 10% and then falls by 10%, the combined factor is 1.10 × 0.90 = 0.99. A starting value of SEK 10,000 then ends at SEK 9,900. Multiplying changes does not mean the overall change must be positive.
A calculator needs assumptions about the rate, time and any deposits. Investor.gov lets users enter such inputs. A completed chart follows its inputs; it does not prove that a real investment will follow the same path.
Write the assumptions before calculating
Record the starting amount, rate, number of periods and what happens to the interest. Also state whether tax and fees are included. Our comparison excludes both and leaves inflation aside. It answers a question about compounding in money terms, not how purchasing power changes.
Check the first and second years by hand before using a shortcut for many years. That can reveal whether the same interest was added twice or a new deposit was mistaken for a return. Continue with Investiq’s lesson guide to plan more clearly defined practice tasks.
Try compound interest with your own numbers
Change the starting amount, yearly interest rate and number of full years to explore the lesson’s two accounts. With interest retained, the formula is starting amount × (1 + rate ÷ 100) raised to the number of years. With each year’s interest moved to an interest-free box, the account and box together equal starting amount × (1 + rate ÷ 100 × number of years).
The same invented rate applies every year and interest is added once at year-end. There are no new deposits. Tax, fees and inflation are also excluded. This compares mathematical assumptions rather than forecasting a result or offering an interest rate from Investiq. Monthly deposits and varying changes in value need different calculations.
Calculated with 10,000.00 SEK, 5 % yearly interest and 3 full years.
- Interest stays in the account
- 11,576.25 SEK
- Account + withdrawn interest
- 11,500.00 SEK
Difference from interest on earlier interest: 76.25 SEK
Withdrawn interest stays in an interest-free box and is included in the comparison. Values are rounded to cents only for display; the model does not round interest each year. An actual account may have different interest and rounding terms.
Follow the amounts year by year
If the table does not fit, scroll it sideways.
| Year | Interest retained | Account + withdrawn interest |
|---|---|---|
| 0 | 10,000.00 SEK | 10,000.00 SEK |
| 1 | 10,500.00 SEK | 10,500.00 SEK |
| 2 | 11,025.00 SEK | 11,000.00 SEK |
| 3 | 11,576.25 SEK | 11,500.00 SEK |
Try it yourself
Start with a fictional SEK 2,000. Interest is 4% per year for two years. What is the final amount if interest stays in the account? What do the account and interest-free box contain together if SEK 80 is withdrawn after each year?
Show the solution and explanation
SEK 2,163.20 with interest retained. SEK 2,160 with the two withdrawals. The difference is SEK 3.20.
2,000 × 1.04 × 1.04 = 2,163.20. With withdrawals, the account stays at 2,000 and the box contains 80 + 80 = 160. The second year’s interest on the first year’s SEK 80 is 80 × 0.04 = 3.20.
Check your understanding
Is three years of compound interest the same as adding 15% in our example?
No. 10,000 × 1.05³ gives SEK 11,576.25. Adding 15% gives SEK 11,500.
Does a compound example promise the same development for a share?
No. Actual changes in value can vary and be negative. The worked example follows its stated assumptions.
Practise with virtual money
Try what you just learned in a practice portfolio with virtual money. You don't deposit any real money.
How the practice portfolio worksKeep learning and practising
More lessons on this topic
Ratios and compound growth
Sources and examples
The sources support the factual explanations. Calculations and exercises were created for this lesson. Amounts and price changes are invented unless stated otherwise.
This material is educational and does not recommend securities to buy. A simulated result does not guarantee a future result.
