ICSE Class 9 Answered
On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and simple interest for a year is Rs 180/-. Find the sum lent out, if the rate of interest in both the case is 10% per annum
Asked by hembromsumi4 | 06 Jul, 2019, 09:21: PM
Expert Answer
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
r = 10%/2 = 5% per conversion period, P = x,
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
Answered by Sneha shidid | 06 Jul, 2019, 09:30: PM
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