Money maths: interest and saving · البرمجة مع مارتن

Money that earns money

Today maths that concerns your wallet. When you put money in a bank, the bank pays you for it. That reward is called interest.

How much you get is decided by the interest rate — a number in percent per year (you will see the short form p. a., Latin per annum, “per year”). A rate of 3 % p. a. means: in a year you get 3 % of the amount you deposited.

The calculation is pure percent work you already know: interest = deposit · rate / 100. A deposit of 5 000 Kč at 3 %: interest = 5000 · 3/100 = 150 Kč. After a year you have 5 150 Kč.

It works the other way too. When you borrow money, you pay the interest. The same formula, the opposite direction of money flow — and rates on loans are usually much higher than on saving. That is why it pays to be able to calculate it before you sign anything.

Today we calculate simple interest: interest always only from the original deposit. The more interesting bit (interest on interest) comes in the next lesson.

Ema earned 8 000 Kč on a job and wants to save for a laptop. Dad shows her an offer: a savings account at 4 % a year. “So how much will the bank add?” Ema counts: “4 % of 8 000… 8000 times 4 divided by 100… 320 Kč a year.” Dad nods: “And if instead you borrowed those 8 000 on a credit card at 20 %, you would pay 1 600 a year. The same maths, the other side of the equation.” Ema writes: save at 4 % yes, borrow at 20 % never without calculating.

💡

Convert percents to money always through one percent: 1 % of 8 000 is 80 Kč, so 4 % is 320 Kč. Three seconds slower, but almost impossible to mix up.

Simple interest step by step

The basic formula: interest per year = deposit · rate / 100.

Step 1: Write what you know: the deposit (how much you put in), the rate (how many % per year), the time (how many years).

Step 2: Calculate the yearly interest. Deposit 10 000 Kč, rate 2 %: interest = 10 000 · 2/100 = 200 Kč.

Step 3: More years with simple interest = yearly interest times the number of years. In 3 years: 3 · 200 = 600 Kč.

Step 4: Balance = deposit + interest. After 3 years: 10 000 + 600 = 10 600 Kč.

Reverse problems (and those turn up in entrance exams):

“The interest was 150 Kč at a rate of 3 %. What was the deposit?” — I look for the base: deposit = 150 · 100/3 = 5 000 Kč.

“A deposit of 4 000 Kč earned 120 Kč in a year. What was the rate?” — I look for percents: 120/4000 = 0.03, so 3 %.

Reality extra: you pay 15 % tax on interest, so of the credited 200 Kč you really keep 170 Kč. In problems you calculate tax only when the question mentions it — but in a bank do not forget it.

Example 1: a year of saving

Question: You put 6 000 Kč into an account at 3 % a year. How much is the yearly interest and how much do you have after a year?

Method: Through one percent: 1 % of 6 000 is 60 Kč. So 3 % = 180 Kč.

Balance after a year: 6 000 + 180 = 6 180 Kč.

Sense check: 180 Kč from six thousand is a small growth — it matches 3 %.

Answer: The interest is 180 Kč, after a year you have 6 180 Kč.

Example 2: how much was the deposit?

Question: The bank credited 250 Kč interest for a year at a rate of 2.5 %. How much was in the account?

Method: I look for the base (100 %), I know 2.5 % = 250 Kč.

One percent: 250/2.5 = 100 Kč.

Base: 100 · 100 = 10 000 Kč.

Check: 2.5 % of 10 000 = 10 000 · 2.5/100 = 250 Kč. It matches.

Answer: There was 10 000 Kč in the account. A reverse problem = a unitary method on percents, nothing new.

Example 3: a loan — the same formula, the opposite direction

Question: A loan of 20 000 Kč at a rate of 15 % a year, you pay it back exactly after a year. How much extra do you pay and how much in total?

Method: Interest = 20 000 · 15/100 = 3 000 Kč.

You return in total: 20 000 + 3 000 = 23 000 Kč.

Compare: the same 20 000 Kč in a savings account at 4 % would earn 800 Kč. The loan costs 3 000 Kč. The bank lives on the difference.

Answer: Extra you pay 3 000 Kč, in total 23 000 Kč. Before every loan calculate this line — it is your defence.

⚠️

A rate is always FOR A PERIOD — read which one. 3 % p. a. means for a year. If you save only half a year, you get a half: 1.5 %. And watch ads: “only 2 % a month” is really 24 % a year — eight times more than a savings account. Always convert the rate to a year, otherwise you compare apples with pears.

Practice: now you do it 🎲

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

Yearly interest from a deposit: deposit times rate divided by a hundred. Write a whole number in Kč.

Practise the questions

On paper

Saving, a reverse problem and one comparison that will help you your whole life.

A deposit of 12 000 Kč, rate 3 % a year. Calculate the yearly interest and the balance after a year and after three years (simple interest).
The interest for a year was 480 Kč at a rate of 4 %. What was the deposit? Do the check.
A loan of 15 000 Kč for a year at a rate of 18 %. How much do you return in total? And how many times more is that than what the same amount would earn in an account at 3 %?
An ad promises “only 1.5 % a month”. Convert to a yearly rate and compare with an ordinary loan at 10 % a year. Which is cheaper?

Now you 💪

You calculate interest through one percent without a calculator.
You can do a reverse problem: from the interest and the rate find the deposit.
You convert a monthly rate to a yearly one and you know why it is تم.

✅

Done when: You have calculated saving for three years, a reverse problem with a check and spotted the ad trap with a monthly rate.

What to take from this lesson

Interest = deposit · rate / 100. A rate p. a. means per year.
Simple interest: each year the same interest from the original deposit.
Reverse problems (find the deposit, find the rate) are a unitary method on percents.
With a loan you pay the interest — the same formula, the opposite direction.
Always convert a monthly rate to a yearly one, otherwise the comparison lies.