Compound interest

Interest on interest

Last time the bank calculated interest always from the original deposit. But real accounts work differently — and much more interestingly. At the end of the year the interest is added to the deposit and the next year that is interest-bearing too. Interest on interest. That is called compound interest.

The difference looks tiny at first. A deposit of 10 000 Kč at 10 %: the first year both the same, +1 000 Kč. The second year simple interest adds 1 000 again, but compound calculates 10 % of 11 000 — so 1 100 Kč. A hundred more.

The third year more. The tenth year much more. Compound interest each year calculates from a bigger and bigger base, so saving speeds up like an avalanche.

It is calculated by multiplying: adding 10 % means multiply by 1.1. Two years = multiply twice: 10 000 · 1.1 · 1.1 = 12 100 Kč.

This mechanism is why it pays to start saving early — and why debts that earn compound interest are so dangerous. Both ways it is an avalanche.

Filip and Tereza test a savings calculator. “I put in 10 000 at ten percent. After a year 11 000, that makes sense,” Filip dictates. “After two years…” he guesses 12 000, but the calculator shows 12 100. “Where is that extra hundred from?” Tereza laughs: “That is interest on last year’s interest. The thousand the bank added started earning on its own.” Filip tries 30 years: 174 494 Kč. “Seventeen times?! And without a single extra koruna deposited?” Exactly. Time is the strongest player with compound interest.

Compound interest step by step

Step 1: Convert the rate to a multiplier. Rate 10 % → multiplier 1.1. Rate 5 % → 1.05. (It is 100 % of the original money plus the interest, so 110 % = 1.1.)

Step 2: Multiply once for each year.

Deposit 10 000 Kč, rate 10 %: after year 1: 10 000 · 1.1 = 11 000 Kč, after year 2: 11 000 · 1.1 = 12 100 Kč, after year 3: 12 100 · 1.1 = 13 310 Kč.

Step 3: Compare with simple interest, so you see the difference. Simple in 3 years: 10 000 + 3 · 1 000 = 13 000 Kč. Compound: 13 310 Kč. Difference 310 Kč — and it grows every year.

Why it speeds up: the base for calculating interest grows every year. The first year only the deposit earns. The second year the deposit + the first interest. The third year the deposit + two interests… A snowball that gathers.

Watch, it works against you too. A debt of 10 000 Kč at 20 % compound: after a year 12 000, after two 14 400, after five almost 25 000 Kč. An unpaid debt with compound interest grows with the same avalanche as saving — only you push it downhill onto yourself.

Example 1: two years step by step

Question: A deposit of 5 000 Kč, rate 10 % a year, compound interest. How much is in the account after two years?

Method: The multiplier for 10 % is 1.1.

After year 1: 5 000 · 1.1 = 5 500 Kč. (Interest 500 Kč.)

After year 2: 5 500 · 1.1 = 6 050 Kč. (Interest 550 Kč — already from 5 500.)

Compare: simple interest would give 5 000 + 2 · 500 = 6 000 Kč. Compound is 50 Kč more — that is interest on the first interest: 10 % of 500.

Answer: After two years there is 6 050 Kč in the account.

Example 2: three years at 5 %

Question: A deposit of 20 000 Kč, rate 5 %, compound interest, 3 years. How much do you save?

Method: Multiplier 1.05.

After year 1: 20 000 · 1.05 = 21 000 Kč. After year 2: 21 000 · 1.05 = 22 050 Kč. After year 3: 22 050 · 1.05 = 23 152.50 Kč.

Sense check: simple interest would give 23 000 Kč. Compound 152.50 Kč more — a small difference in three years, but it grows every year.

Answer: After three years there is 23 152.50 Kč in the account.

Example 3: a debt as an avalanche

Question: An unpaid debt of 8 000 Kč is charged 20 % a year (compound). How much do you owe after three years of not paying?

Method: The multiplier for 20 % is 1.2.

After year 1: 8 000 · 1.2 = 9 600 Kč. After year 2: 9 600 · 1.2 = 11 520 Kč. After year 3: 11 520 · 1.2 = 13 824 Kč.

Answer: The debt grew to 13 824 Kč — almost by three quarters. The same maths that saves for you can work against you. That is why debts are paid at once and why you calculate before you sign.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 开始 with ten. When it goes well, add more.

Two years of compound interest at 10 %: multiply by 1.1 and once more by 1.1. Write a whole number in Kč.

Practise the questions

On paper

Calculate year by year, one line for each year. You will see the avalanche grow.

1. A deposit of 10 000 Kč, 10 % compound: calculate the balances after year 1, 2 and 3. Next to them write simple interest and the differences.

2. A deposit of 50 000 Kč, 4 % compound, 2 years. How much is in the account? (Multiplier 1.04.)

3. A debt of 5 000 Kč, 25 % a year compound, 3 years without paying. How much do you owe? Round to koruna.

4. A thinking question with a calculation: what is more after 2 years — 10 000 Kč at 20 % compound, or 12 000 Kč at 5 % compound?

Now you 💪

1. You can convert a rate to a multiplier (5 % → 1.05) and explain why.
2. You calculate each year separately and you know where interest on interest comes from.
3. You understand that compound interest works for you with saving and against you with a debt.

What to take from this lesson

• Compound interest = the interest is added to the deposit and then earns too.
• Adding p % means multiply by (1 + p/100). Each year one multiply.
• Two years at 10 % is times 1.21, not times 1.2.
• The longer the time, the bigger the lead of compound interest — start saving early.
• With debts it is an avalanche against you. Calculate before you sign.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款