Each of us got acquainted with the concept of percentage, as the relationship of any share to the whole, back in school, but in practice, even primitive mathematical operations with percentages can be performed only by those who are faced with similar tasks by occupation. And marketers are happy to use it.

We all know perfectly well how shop assistants can turn a real 25% discount into 50%, and bankers, on the contrary, sell loans at 30% with 15% specified in the terms of the agreement. At the same time, it is not so difficult to learn how to calculate real percentages, and below we give several basic calculation methods for frequently encountered situations.

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## How to convert numbers to percentages and vice versa

These are fairly simple operations that in most cases do not require complex calculations. Most often, to convert a number to a percentage and vice versa, the numerical equivalent of 1% or 10% is determined by simply dividing the base amount (whole) by 100 or 10.

For example, having a 4% discount card in a store, you can quite easily estimate the final cost of the product.

A smartphone costs 25,000 rubles, 1% of this amount will be: 25,000 / 100 = 250, that is, 1% = 250 rubles, respectively, our 4% discount will save 250 × 4 = 1,000 rubles when purchasing this product.

Naturally, it will not be difficult to convert the numbers to percentages:

If your favorite chocolate cost 500 rubles, and now it costs 350 rubles, then to calculate the discount in percentage we perform the following actions: define 1% = 500/100 = 5 rubles, then calculate the percentage of the new price from the old one: 350 rubles / 5 rubles = 70%, and in a simple way we get the size of the discount: 100% – 70% = 30%.

Sometimes for working with large “round” numbers it is more convenient to use the calculation of 10% instead of 1%.

For example, you put 700 thousand rubles on a deposit at 20% per annum and want to calculate how much you will receive as a result. We calculate 10%: 700,000/10 = 70,000 rubles, respectively 20% per annum = 70,000 × 2 = 140 thousand rubles of your profit.

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## How to calculate percentages in proportions

Another common life situation when we need to compare the percentages among ourselves. For this, an equation of the form is usually used **X / Y = A / B**, which can be read as: “the share of X refers to the whole Y as well as the share of A refers to the whole B”.

Let’s give an example:

You are going to paint the walls and you know that in order to obtain the desired shade, you need to dilute 400 grams of pigment in 5 liters of water, but during the last mixing you find that only 300 grams of the coloring matter remains, how much water should you add?

First, let’s calculate the percentage of pigment residue:

400 grams / 100% = 300 / P% (desired percentage)

400 grams is 100% the same as 300 grams is P%. That is, 400/100 = 300 / P%. To simplify the calculations in your head, remember that X / Y = A / B also means that X × B = Y × A, which means in our example 400 × P% = 100 × 300, P% = 30000/400 = 75 %.

Now we calculate the amount of water required for the last mixing and again use the proportion for clarity:

5 liters / 100% = X (required amount of water) / 75%

X × 100 = 5 × 75,

X = 375/100 = 3.75 liters.

We now know that 300 grams of pigment refers to 3.75 liters of water, just as 400 grams refers to 5 liters.

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## How to calculate the interest rate on a loan (interest per annum)

Bankers are very fond of playing with numbers and it is almost impossible to calculate the loan rate in advance – even if, under the threat of torture, find out a specific value, then it will most likely be changed later through hidden payments or some special conditions prescribed in the agreement.

Imagine the following situation, you repaid a loan for 80 thousand rubles in a bank that you used for a year, eventually paying 115,500 rubles. Now you have a choice: to get a similar loan for a year and a half in the same bank to buy a new iPhone XS, or take a smartphone in installments at 4% per month. Naturally, in order to determine the best option, we need the value of the monthly interest rate on a bank loan in order to compare it with interest on installments. For this we use a universal formula:

**R × 100 = I / S × P**where:

**R** = desired interest rate;**I** = overpayment on the loan;**S** = loan amount;**P** = time period (year, month, week).

For our first loan we have:

I = 115,550 – 80,000 = 35,550 rubles overpayment. Accordingly, R × 100 = 35,550 rubles / 80,000 rubles × 12 months = 35,500 / 960,000 = 0.03703125. Multiply by 100 and we get a monthly rate of 3.7%, which is more profitable compared to a 4% installment plan in a store.

Now let’s calculate the amount of overpayment for a year and a half of using the loan:

*I = R (0.037) × S (80,000 rubles) × 18 months = 53,280 rubles*…

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## How to calculate interest using a calculator (on iPhone, tablet, etc.)

Counting in your head is, of course, very useful, but sometimes it is much more convenient to get a smartphone and perform all the actions with a couple of movements in the calculator application. For instance:

- We consider a 4% discount on the purchase of a smartphone worth 25,000 rubles (we find a percentage of the number) – enter
**25,000 × 4**, press the sign**“%”**and**“=”**, we get**1000**discount rubles; - In the example with a deposit of 700 thousand rubles at 20% per annum – we enter
**700,000 × 20**, press the sign**“%”**and**“=”**, we get**140,000**rubles of profit. Here it can be noted that if in the expression replace**“×”**on**“+”**, respectively,**700,000 + 20**and press**“%”**and**“=”**, then in the answer we get immediately**the sum of the original number (i.e. 700,000) + 20% (i.e. 140,000)**, i.e**840,000**rubles.

Etc.

In the most difficult situations, special calculators with ready-made formulas that can be used online will come to the rescue. For example, on the sites planetcalc.ru and allcalc.ru you can find special programs for calculating loan and deposit rates, mortgages, subsidies, etc.

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