A very important application of the concept of percentage is in calculating interest.
You may have heard people saying that some bank paying $5\%$ interest some other paying $7\%$ interest.
When you deposit money in your bank, the bank usually pays some interest for that money, similarly, when you take a loan from a bank, the bank charges some interest from you.
II. Concept
Interest, is commonly expressed as some percentage per annum. This means that the bank will add to your account, the given percentage of your initial deposit amount every year.
Let us look at an example before we get to the actual formula,
Let us say your bank pays $8\%$ simple interest per annum, and you deposit $Rs\ 200$ in your bank for a period of two years.
Every year, the bank will add $8\%\ of\ 200 = \dfrac{8}{100} \times 200 = Rs\ 16$ to your account.
So, at the end of two years, your account will have $200 + 16 \times 2 = Rs\ 232$ in it.
Let us take one more example:
What is the simple interest on $Rs\ 800$ for $5$ years at the rate $9\%$ per annum?
For $1$ year the interest is $800 \times \dfrac{9}{100} = 72\ Rs$
Hence, for $5$ years the interest is $5 \times 72 = 360\ Rs$
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Before we see the derivation of the formula, let us look at the common terminology used in the context of interest.
The amount you deposit initially with the bank is call the $\underline{Principal}$ and is commonly denoted using $P$
The rate at which the bank pays you interest is called the $\underline{Annual\ Interest\ Rate}$ or the $\underline{Rate\ Of\ Interest\ Per\ Annum}$ and is denoted using $R$
The number of years which for which the money is deposited with the bank is called the $\underline{Period}$ and is denoted using $N$ or $n$.
The final amount which the depositor gets back, that is the original principal and the interest earned during the entire period is called the $\underline{Final\ Amount}$ or $\underline{Amount}$ and is commonly denoted as $A$.
Now we can look at the formula.
Let's say you deposit principal $P$ with a bank which pays $R\%$ simple interest per annum.
Interest amount for the $1^{st}$ year = $P \times \dfrac{R}{100}$ ,
$\therefore$ total interest after $1$ year = $P \times \dfrac{R}{100} = \dfrac{PR}{100}$
Interest amount for the $2^{nd}$ year = $P \times \dfrac{R}{100}$,
$\therefore$ total interest after $2$ years = $\dfrac{PR}{100} + \dfrac{PR}{100} = \dfrac{2PR}{100}$
$...$
Interest amount for the $n^{th}$ year = $P \times \dfrac{R}{100}$
$\therefore$ total interest after $3$ years = $\dfrac{nPR}{100}$
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Therefore the total amount that you get back after $n$ years, including your original deposit of $P$ will be:
$P + \dfrac{nPR}{100}$
Now let us try the following problem:
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