Question
Download Solution PDFThe difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375. What will be the principal?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375
Formula used:
Simple Interest = (P × N × R)/100
Compound Interest = [P(1 + (r/200))T] - P (for compounded half yearly)
Calculation:
Let P be the Principal,
S.I = (P × 1 × 25)/100 = P/4
C.I = [P(1 + (25/200))2] - P ( T = 2 ∵ compounded half yearly for 1 year)
⇒ C.I = 17P/64
Now, C.I - S.I = (17P/64) - (P/4) = P/64
⇒ P/64 = 4375
∴ P = 64 × 4375 = 280000
Shortcut TrickFormula used:
CI - SI = P(R/100)2
Rate (R) = 25%/2 due to the compounded half-yearly.
⇒ 4375 = P (25/200)2
⇒ P = 4375 × 64
⇒ P = 280,000
∴ The sum is Rs. 280,000.
Last updated on Jun 6, 2025
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