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Question
A sum of money is lent at 8% per annum compound interest. If the interest for the second year exceeds that for the first year by Rs. 96, find the sum of money.
Solution
Let money be Rs100
For 1st year
P = Rs. 100; R = 8% and T = 1 year.
Interest for the first year = Rs. `[ 100 xx 8 xx 1]/100` = Rs. 8
Amount = Rs. 100 + Rs. 8 = Rs. 108
For 2nd year
P = Rs.108; R = 8% and T= 1year.
Interest for the second year= Rs. `[ 108 xx 8 xx 1]/100` = Rs. 8.64
Difference between the interests for the second and first year = Rs. 8.64 - Rs. 8 = Rs. 0.64
Given that interest for the second year exceeds the first year by Rs. 96.
When the difference between the interests is Rs. 0.64, principal is Rs. 100
When the difference between the interests is Rs96, principal = Rs. `[96 xx 100]/0.64` = Rs. 15,000.
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