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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.
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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