Interest in one sentence · Code with Martin

Interest is a percent of a deposit for a year. One sentence, one calculation — and you understand saving and loans.

The bank pays you a percent. Or you pay it.

Interest sounds like a word for adults, but it is an ordinary percent with a calendar. Interest is a percent of the amount you deposit (or borrow) for one year.

You put 2 000 Kč in the bank at 3% a year. In a year the bank adds 3% of 2 000, so 60 Kč. You have 2 060 Kč. That is all.

The amount you put in is called the deposit (or the principal). The percent is called the interest rate. And the word “a year” (sometimes written “p.a.”) says how long it takes before the interest is added.

It works the other way too — and that is why we teach this lesson. When someone borrows, they pay the interest. A loan of 2 000 Kč at 20% a year means paying back 2 400 Kč. The same calculation, the opposite direction of money. Who can calculate interest will not be fooled by an advert for a “great loan”.

Ema complains at grandma’s that she does not want to save: “Money in a piggy bank just sits there.” Grandma pulls out an old passbook: “In the bank it does not sit. The bank pays me 3% a year for lending it my money.” Tereza counts: grandma’s 5 000 Kč × 0.03 = 150 Kč a year. “That is little,” Ema wrinkles her nose. Grandma nods: “For a year, little. But free, and every year. And most of all —” she taps a loan flyer from the paper, “this one wants 19%. Count how much the person who borrows 5 000 pays.” Tereza: “950 Kč. A year!”

💡

With saving and with a loan, ask for two numbers: how many percent and for how long. Interest without time means nothing — 5% a year and 5% a month is a huge difference.

How to calculate interest for a year and for part of a year

Interest for one year:

interest = deposit × rate (as a decimal).

Deposit 4 000 Kč, rate 2.5%: interest = 4 000 × 0.025 = 100 Kč. After a year you have deposit + interest = 4 100 Kč on the account.

Interest for part of a year is cut by time. For half a year a half, for 3 months a quarter. Deposit 4 000 Kč at 2.5% for 6 months: 100 × 1/2 = 50 Kč.

More years (simple interest): interest times the number of years. Three years with interest of 100 Kč a year = 300 Kč. (Banks often count so-called compound interest, where even the added interest earns interest — we leave that for later. For an estimate, simple is enough.)

A loan: the same formula, but you pay the interest. You pay back = loan × (1 + rate). Loan 10 000 Kč at 15%: you pay back 10 000 × 1.15 = 11 500 Kč.

The method for every question: 1) find the deposit/loan, 2) convert the rate to a decimal, 3) multiply, 4) decide whether the interest is added to you, or to your debt.

Deposit 8 000 Kč, interest 4% a year. How much do you have after a year?

Step 1: deposit 8 000, rate 4% = 0.04.

Step 2: interest = 8 000 × 0.04 = 320 Kč.

Step 3: on the account there will be 8 000 + 320 = 8 320 Kč.

Result: 8 320 Kč. Check via 1%: a hundredth of 8 000 is 80, four hundredths 320. That checks out. Notice the question “how much do you have” wants deposit + interest, not just interest — read carefully what the question asks.

Interest for half a year on 6 000 Kč at a rate of 3% a year

Step 1: yearly interest: 6 000 × 0.03 = 180 Kč.

Step 2: half a year = half of the yearly interest: 180 : 2 = 90 Kč.

Result: 90 Kč. The word “a year” in the rate is the key — the rate is for a whole year, a shorter time gets only a proportional part. For 3 months (a quarter of a year) the interest would be 45 Kč, for 2 years 360 Kč.

A loan of 12 000 Kč for a year at a rate of 18%. How much do you pay back?

Step 1: interest = 12 000 × 0.18 = 2 160 Kč.

Step 2: I pay back the loan and the interest: 12 000 + 2 160 = 14 160 Kč.

Shortcut: 12 000 × 1.18 = 14 160 Kč.

Result: 14 160 Kč. For a year of using someone else’s money you pay 2 160 Kč extra — that is the price of the loan. Compare: a savings account gives you 3–4%, a loan takes as much as 18%. That is why it pays to save first and borrow as little as possible.

⚠️

A rate without a period is a trap. “Only 2% a month” is really around 24% a year — twelve times more than it sounds. Always convert the rate to a year, only then compare offers.

Practice: now you do it 🎲

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

Interest is a percent of a deposit — train a percent of a number. Write only the number, without Kč and without %.

Practise the questions

On paper: a little bank

Calculate without a calculator where you can. For each question write who pays whom.

Deposit 3 000 Kč, rate 2% a year. How much is the interest for a year and how much will be on the account after a year?
How much is the interest on 10 000 Kč at 3.6% a year for a quarter of a year (3 months)?
A loan of 8 000 Kč at 25% a year. How much do you pay back after a year? Calculate the long way (interest separately) and the shortcut (times 1.25).
An advert promises “a mere 1.5% a month”. Convert the rate to a year and write in one sentence why the advert sounds better than the truth.

Now you 💪

I can say what interest is: a percent of a deposit or a loan for a given time, usually a year.
I calculate interest for a year and its proportional part for half a year or a quarter of a year.
I know that with a loan I pay the interest, and I can calculate the total amount paid back.

✅

Done when: Four questions done, on each it is written who pays whom, and converting the monthly rate to a yearly one gave you 18%.

What to take from this lesson

Interest = deposit × rate (a decimal) for a year.
A shorter time = a proportional part of the yearly interest.
A loan: you pay back loan × (1 + rate). Interest is the price of someone else’s money.
Always convert the rate to a year, otherwise you compare things that cannot be compared.
Saving adds a percent to you, a loan takes it from you.