Page 292 - ICSE Math 8

SIMPLE INTEREST AND COMPOUND INTEREST

Simple Interest: The extra amount paid or earned by a borrower or a lender is known
as simple interest or interest.
P × RT× P = Principal, R = Rate%, T = Time and
Simple Interest, I = I = Simple Interest or Interest
100
100 × I 100 × I 100 × I
P = R = T =
×
RT PT× P × R
 1 + RT 
Amount, A = P + I = P  
 100 

Compound Interest when the Interest is compounded

Annually
n   R  n  

R 
A = P 1 +  ; C.I. = P 1 +   − 1 

 100   100     
When the rates are different for different years, i.e. R1%, R2%, R3%,
…, Rn% for 1st, 2nd, 3rd, …, nth year respectively

A = P 1 +   R 1     1 + R 2     1 + R 3   … 1 + Rn   ; C.I. = A – P

 100   100   100   100 
 lR 
l  R  n  m 
When time is in fraction, n : A = P 1 +    1 + 
m  100   100 
   

Half-Yearly
Rate becomes half and time doubles

 R  2n   R  2n  
A = P 1 +  ; C.I. =P 1 +   − 1 

 2 + 100   200     
Quarterly
Rate becomes quarter and time 4 times

A = P 1 + R   4n ; C.I. = P 1 +    R   4n − 1   

 4 100  ×  400     

Appreciation and Depreciation
P = Initial asset value, R(–R) = Rate of appreciation/depreciation
 R  n  R  n
A = P 1 +  or P 1 − 


 100   100 
Asset value after n yrs for different rates,
 R 1   R 2   R 3   Rn 
Asset value = P 1 +    1 +   1 +  …  1 +  , or,
 100   100   100   100 
 R 1   R 2   R 3   Rn 
Asset value = P 1 −    1 −   1 −  …  1 − 
 100   100   100   100 

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