How to calculate percentage of interest
In many applications, the value of anyfor example, wages, first increases by X%, and then by another Y%. How to calculate the percentage of interest and find out how much the initial value of this value has changed?
Salary is growing
At first glance it seems that you just needfold X% and Y%. But the calculations show that this is not so. For example, let's take a salary increase, which initially amounted to 30,000 rubles. In the first year, it grew by 20%, and in the second - by another 10%. How much did it grow over two years and what did it become?
- 20% of 30,000 are (30,000 * 20) / 100 = 6,000; therefore after the first year the salary became 30 000 r. + 6,000 rubles. = 36,000 rubles.
In the second year, the salary increased by another 10%, but these 10% should not be counted from the initial salary of 30,000 rubles, but from the one that developed in a year, that is, from 36,000 rubles.
- 10% of 36,000 is (36,000 * 10) / 100 = 3,600; therefore after the second year the salary became 36 000 r. + 3 600 r. = 39 600 r.
To find out how much the salary grew over 2 years, you need a salary after the second year of 39 600 rubles. divided into an initial salary of 30,000 rubles. and multiply by 100%:
for 2 years the salary has grown on (39 600/30 000) * 100% = 32%
The goods become cheaper
Now we take the case when the quantitydecreases. For example, the price of goods fell by 40%, and then another 25%. How much did the price of the goods fall from the original price? How much did the product cost if its initial cost was 3,000 rubles?
- 40% of 3,000 are (3,000 * 40) / 100 = 1,200; so after the first reduction in price, the goods will cost 3,000 rubles. - 1 200 р. = 1 800 p.
The second time, the goods are cheaper by 25%, but not from the initial price, but from the price with a 40% discount, that is, from 1,800 r.
- 25% of 1,800 is (1,800 * 25) / 100 = 450; so after the second reduction in price, the goods will cost 1 800 rubles. - 450 r. = 1 350 r.
To find out how much the goods have fallen in price for two markdowns, the difference between the initial price of 3,000 rubles is needed. and the final price of 1 350 rubles. divide by the initial price and multiply by 100%:
for 2 times the commodity has fallen in price on ((3 000 - 1 350) / 3 000) * 100% = (1 650/3000) * 100% = 55%.
In both examples, the amount of interest on which the value was changed does not coincide with its change as a whole.
Finally, a mixed example, when the value firstdecreases, and then grows. Salary of 40 000 r. first reduced by 10%, and then increased by 10%. Has the salary changed, and if so, by what percentage?
- 10% of 40 000 is 4 000; so after a decrease in wages, it became 40,000 rubles. - 4 000 rubles. = 36,000 rubles.
- 10% of 36 000 is 3,600; so after the increase the salary became 36 000 rubles. + 3 600 r. = 39 600 r.
As a result of this mathematical focus, wages are notreturned to the initial value, and decreased by (400 / 40,000) * 100% = 1%, where 400 r. - this is the difference between the initial and final wages, 40,000 rubles. - this is the initial salary.