Theory:

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 by the number of days that elapse between payments.
  • This type of interest usually applies to automobile loans or short-term loans,
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) is 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+ISubstitutetheIvalueintheaboveequation.A=P+(P×n×r100)IfwetakethecommontermPoutthenwewillget:A=P+(1+n×r100)WeknowthatAmount=Interest(I)+Principal(P)SoI=AP
 
Another formula can be derived based on I=P×n×r100.
r=100×Ip×nAndn=100×Ip×rp=100×Ir×n