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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
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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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