Mathematics for FinancePYQ June 19Question 1194 of 512
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If P=Rs. 2,96\displaystyle P = \text{Rs. }2,96, and R=8%\displaystyle R = 8\% compounded annually then P=\displaystyle P =

Options

ARs. 14,000\displaystyle \text{Rs. }14,000
BRs. 15,000\displaystyle \text{Rs. }15,000
CRs. 16,000\displaystyle \text{Rs. }16,000
DRs. 17,000\displaystyle \text{Rs. }17,000
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Correct Answer

✅ Option b — Rs. 15,000\displaystyle \text{Rs. }15,000

All Options:

  • ARs. 14,000\displaystyle \text{Rs. }14,000
  • BRs. 15,000\displaystyle \text{Rs. }15,000
  • CRs. 16,000\displaystyle \text{Rs. }16,000
  • DRs. 17,000\displaystyle \text{Rs. }17,000

Detailed Solution & Explanation

**Derivation of Principal** Given: - The relationship: P⋅i2=96\displaystyle P \cdot i^2 = 96 - Rate (R\displaystyle R) = 8%\displaystyle 8\% compounded annually - Here, i=R100=0.08\displaystyle i = \frac{R}{100} = 0.08 represents the periodic rate. - In financial math, the equation P⋅i2=Difference\displaystyle P \cdot i^2 = \text{Difference} represents the difference between compound interest and simple interest for 2\displaystyle 2 years. **Step 1: Set up the equation with the given rate** P⋅(0.08)2=96P \cdot (0.08)^2 = 96 **Step 2: Solve for P\displaystyle P** P⋅0.0064=96P \cdot 0.0064 = 96 P=960.0064P = \frac{96}{0.0064} P=96×1000064P = \frac{96 \times 10000}{64} P=15,000P = 15,000 Hence, **Option B** is the correct answer.

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