Simple interest on a given amount is always ____ than or ____ to the compound interest on the same amount for the same period of time and at the interest rate per annum.

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Accepted Answer

Simple interest on a given amount is always than or to the compound interest on the same amount for the same period of time and at the interest rate per annum.

S.I.=
    
     P×R×T
    
     100

The formula for compound interest is,

C.I.=P

1+
        R
        
         100

t
   
   −P
  Therefore, by the definition of simple interest and compound interest we can say that

S.I.<C.I.
   because, in simple interest, interest is charged for the principal amount but in compound interest, the interest charged on it is for the principal and accrued interest.If the interest is for 1 year then Simple Interest is,

S.I.=
    
     P×R×T
    
     100

Therefore,

S.I.=
    
     P×R×1
    
     100
   
   =
    
     P×R
    
     100

And, Compound interest is,

C.I.=P

1+
        R
        
         100

t
   
   −P
   Therefore,

C.I.=P

1+
        R
        
         100

1
   
   −P=P+
    
     P×R
    
     100
   
   −P

⇒C.I.=
    
     P×R
    
     100

That means, in this case

S.I.=C.I.
   From the above explanation, we have seen that Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same period of time and at the interest rate per annum.

Simple interest on a given amount is always than or to the compound interest on the same amount for the same period of time and at the interest rate per annum.

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