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Question
The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1320 and for the third year is Rs. 1452. Calculate the rate of interest and the original sum of money
Solution
C. I. for the third year = Rs. 1452.
C. I. for the second year = Rs. 1320
S.I. on Rs. 1320 for one year = Rs. 1452 – Rs. 1320 = Rs. 132
∴ Rate of Interest = `(132xx100)/(1320) = 10%`
Let P be the original sum of money and r be the rate of interest.
Amount after 2 years – Amount after one year = C.I. for the second year.
`P(1 + 10/100)^2 - P(1 + 10/100) = 1320`
`=> P[(110/100)^2 - (110/100)] = 1320`
`=> P[(11/10)^2 - 11/10] = 1320`
`=> P [(121/100) - 11/10] = 1320`
`=> P == (1320 xx 100)/111 = Rs 12000`
Thus, rate of interest is 10% and original sum of money is Rs.12,000
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