Question
A certain sum of money invested at 20% per annum for 2
years compounded annually, but if interest would have been compounded half yearly on the same amount, then Rs. 241 more interest would have been received. Find the sum of money invested.Solution
Let the certain amount of money invested be Rs.‘P’.
When interest is compounded yearly,
So, CI = P(1 + 20/100) 2  – P = P[(1 + 20/100)  2  – 1] = P(1.44 – 1) = 0.44 × P
When interest is compounded half yearly,
And, CI = P(1 + 10/100)  4  – P = P[(1.1)  4  – 1] = P(1.4641 – 1) = 0.4641 × P
According to question, 0.4641×P – 0.44×P = 241
0.0241×P = 241
P = 241/0.0241 = 10000
Therefore, the certain amount of money invested is Rs. 10000.
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