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.

Answer 1

(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 1^st year = 10% of Rs.100= Rs.10

⇒ Amount in one year = Rs. 100 + Rs. 10 = Rs. 110
Similarly, C.I. for 2^nd year = 10% of Rs. 110 = Rs. 11
When C.I. for 2^nd year is Rs. 11, sum = Rs. 100
When C.I. for 2^nd year is Rs. 1089, sum = Rs. `[ 100 xx 1089 ]/11`
= Rs. 9,900.