Page 127 - ICSE Math 8

Computation of compound interest when interest is compounded annually

If, P is Principal, R% is Rate of interest per year and n is number of years then amount at the end of n years
 R  n
is given by A = P 1+ 100  .



 R  n    R  n 
Then, C.I. = A – P = P 1+ 100  – P = P   1+ 100 − 1 




 
 
Example 10: The simple interest on a certain sum of money at the rate of 4% per annum for 3 years is ` 1,200.
Find the compound interest on the same amount at the rate of 10% per annum for 3 years.
Solution: Let the principal (P) be ` x.
PR T××
We know that, I =
100
x××43 12x 1 200 100, ×
fi 1,200 = fi = 1,200 fi x = = 10,000
100 100 12
\ Principal (P) = ` 10,000

Now, P = ` 10,000, R = 10%, n = 3 years

 R  n  10  3  1  3  11 3
A = P 1+ 100  = ` 10,000 1+ 100 = ` 10,000 1+ 10 = ` 10,000   10 








 11 11 11
= ` 10 000, × 10 × 10 × 10  = ` 13,310


Hence, C.I. = A – P = ` (13,310 – 10,000) = ` 3,310
Computation of compound interest when the interest is compounded half-yearly
 R
If, P = Principal R% =   % per half year Maths Info
2 

 R  2n When the interest is compounded half-
n = 2n A = P 1+ 2 100×   yearly, the rate of interest becomes


 R  % and the time doubles (2n).
2

 R  2n    R  2n  half  
 
Then, C.I. = A – P = P 1+ 2 100×   – P = P    1+ 200 − 1 



 
 
Example 11: Find the compound interest on ` 50,000 for 2 years at the rate of 8% per annum compounded
half-yearly.
Solution: P = ` 50,000, n = 2 years, R = 8% per annum
 R  2n  8  2 × 2  8  4
\ Amount after 2 years = P 1+ 200  = ` 50,000 1+ 200 = ` 50,000 1+ 200 






 1  4  26 4
= ` 50,000 1+ 25  = ` 50,000   25



 26 26 26 26
= ` 50 000, × 25 × 25 × 25 × 25 = ` 58,492.93



\ C.I. = A – P = ` (58,492.93 – 50,000) = ` 8,492.93
115