Question
Download Solution PDFThe difference between compound and simple interests on a certain sum of money at the interest rate of 20% per annum for \(1{1 \over2}\) years is Rs. 6,200, when the interest is compounded semi-annually. Find the sum of money.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The difference between CI and SI = Rs. 6200
Time = \(1{1 \over2}\) years
Rate = 20%
Compounded semi-annually
Concept Used:
SI = PRT/100
CI = P{[1 + R/100]T - 1}
where, P = Principal
R = Rate of interest
T = Time period
Calculation:
SI = (P × 20 × 3)/(100 × 2)
⇒ SI = 3P/10
As the Interest is compounded semiannually, R = 20/2 = 10% and Time period = 3
⇒ CI = P{[1 + 10/100]3 - 1}
⇒ CI = P{[1 + 1/10]3 - 1}
⇒ CI = P{[11/10]3 - 1}
⇒ CI = 331P/1000
According to Question,
⇒ CI - SI = 6200
⇒ 331P/1000 - 3P/10 = 6200
⇒ (331P - 300P)/1000 = 6200
⇒ 31P/1000 = 6200
⇒ P = 200000
Therefore, the sum of money is Rs. 200000.
Last updated on Jun 12, 2025
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