Mathematics for FinanceMTP Oct 21, ICAI SMQuestion 1336 of 512
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A sum of 46,875\displaystyle 46,875 was lent out at simple interest and at the end of 1\displaystyle 1 year 8\displaystyle 8 months, the total amount was 50,000\displaystyle 50,000. Find the rate of interest per annum.

Options

A8%\displaystyle 8\%
B4%\displaystyle 4\%
C12%\displaystyle 12\%
DNone
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Correct Answer

✅ Option b — 4%\displaystyle 4\%

All Options:

  • A8%\displaystyle 8\%
  • B4%\displaystyle 4\%
  • C12%\displaystyle 12\%
  • DNone

Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Principal (P\displaystyle P) = Rs. 46,875\displaystyle \text{Rs. }46,875 - Future Value (A\displaystyle A) = Rs. 50,000\displaystyle \text{Rs. }50,000 - Time (T\displaystyle T) = 1\displaystyle 1 year and 8\displaystyle 8 months = 1+812=1+23=53\displaystyle 1 + \frac{8}{12} = 1 + \frac{2}{3} = \frac{5}{3} years **Step 1: Calculate Simple Interest (SI\displaystyle SI)** SI=A−P=50000−46875=Rs. 3,125SI = A - P = 50000 - 46875 = \text{Rs. }3,125 **Step 2: Solve for Rate (R\displaystyle R)** SI=P×R×T100SI = \frac{P \times R \times T}{100} 3125=46875×R×531003125 = \frac{46875 \times R \times \frac{5}{3}}{100} 3125=468.75×53R3125 = 468.75 \times \frac{5}{3} R 3125=781.25R3125 = 781.25 R R=3125781.25=4% per annumR = \frac{3125}{781.25} = 4\% \text{ per annum} Hence, **Option B** is the correct answer.

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