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Simple Interest \((I)\):
  • Simple interest is a quick and easy method of calculating the interest charge on loan.
  • Simple interest is determined by multiplying the interest rate by the principal and by the number of days that elapse between payments.
  • This type of interest usually applies to automobile loans or short-term loans.
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Derivation of the formula to calculate the Simple interest (\(I\)):
 
First, take \(P\) as the principal or sum and \(r\%\) as a rate percent per annum. On every \(₹100\) borrowed, the interest paid is \(₹r\).
 
Therefore, on \(₹P\) borrowed, the interest paid for one year would be =P×1×r100.
 
Then the interest period for two years =P×2×r100.
 
Then the interest period for three years =P×3×r100 and so on.
 
If the time period is '\(n\) ' number of years, the formula will be I=P×n×r100.
 
Basic Formulae:
 
Amount (\(A\)) :     
If the principal amount \((P)\), and simple interest \((I)\) are given, then we can find out the amount, by adding the principle and simple interest.
A=P+I
 
Simply rearranging both the formula as per requirement, we can find all the variants in the formula.
 
I=P×n×r100;A=P+I
 
Substitute the "\(I\)" value in the above equation.
 
A=P+(P×n×r100)
 
If we take the common term \((P)\) out then we will get:
 
A=P×(1+n×r100)
 
\(\text{Amount} =\) \(\text{Principal} +\) \(\text{Interest}\).
 
So, \(I = A – P\).
 
Another formula can be derived based on I=P×n×r100.
 
r=100×Ip×n
 
And, n=100×Ip×rp=100×Ir×n.