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Question
The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money.
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Solution
(i) C.I. for second year = Rs. 1,089
C.I. for third year = Rs. 1,197.90
∵ Difference between the C.I. of two successive years
= Rs. 1,197.90 - Rs. 1089 = Rs. 108.90
⇒ Rs. 108.90 is the interest of one year on Rs.1089.
∴ Rate of interest = Rs. `[ 100 xx "I"]/["P" xx "T" ]` %
= `[100 xx 108.90]/[1089 xx 1]` % = 10%
(ii) Let the sum of money = Rs.100
∴ Interest on it for 1st year = 10% of Rs.100= Rs.10
⇒ Amount in one year = Rs. 100 + Rs. 10 = Rs. 110
Similarly, C.I. for 2nd year = 10% of Rs. 110 = Rs. 11
When C.I. for 2nd year is Rs. 11, sum = Rs. 100
When C.I. for 2nd year is Rs. 1089, sum = Rs. `[ 100 xx 1089 ]/11`
= Rs. 9,900.
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