Question
Mon June 11, 2012 By: Bhavna

on a certain sum of money the difference between the compound interest for a year payable half-yearly and the simple interest for a year is Rs 180.Find the sum lent out the rate of interest in both the cases being 10%

Expert Reply
Mon June 11, 2012
Let the principal, P = Rs.x, r = 10%, t = 1 year
 
Using S.I. = Prt/100,
S.I. = Rs.(x × 10 × 1)/100 =Rs.x/10
 
No of conversion period, n = 2 × 1 = 2,
r = 10%/2 = 5% per conversion period, P = x,
 
Using C.I. = P [(1 + r/100)n– 1],
C.I. = Rs.x [(1 + 5/100)2– 1]
= Rs.x(21/20 ×21/20 – 1)
= Rs.x(441/400 – 1)
= Rs.(41/400)x

As per problem, C.I. – S.I. = Rs.180
Or, Rs.(41/400)x – Rs.x/10 = 180
Or, Rs.(41/400 – 1/10)x = 180
Or, Rs.x/400 = 180
Or, x = Rs.180 × 400 = Rs.7200
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