﻿
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%

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
Related Questions
Sun May 15, 2016

# (please do without using formula) if a sum of money placed at c.i doubles itself in 4 yrs. in how many yrs will it be eight times? Divide Rs.21866 into two parts such that the amount of one in 3 yrs is same as the amount of the second in 5 yrs.The rate of c.i being 5% p.a.

Mon March 28, 2016

﻿