Mathematics of FinanceMCQPYQ May 20Question 1300 of 512
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A sum of $46,875$ was lent out at simple interest and at the end of $1year\displaystyle year8$ months the total amount was $50,000$. Find the rate of interest percent per annum.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — 4%\displaystyle 4\%

All Options:

  • A5%\displaystyle 5\%
  • B6%\displaystyle 6\%
  • C4%\displaystyle 4\%
  • D8%\displaystyle 8\%

Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Principal (P\displaystyle P) = Rs. 46,875\displaystyle Rs. \displaystyle \text{Rs. }46,875 - Future Value (A\displaystyle A) = Rs. 50,000\displaystyle Rs. \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 + 812=1+23=53\displaystyle \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 = Rs. \displaystyle \text{Rs. }3,125 **Step 2: Solve for Rate (R\displaystyle R)** SI=P×R×T100SI = P×R×T100\displaystyle \frac{P \times R \times T}{100} 3125=46875×R×531003125 = 46875×R×53100\displaystyle \frac{46875 \times R \times \frac{5}{3}}{100} 3125=468.75×53R3125 = 468.75 ×\displaystyle \times 53\displaystyle \frac{5}{3} R 3125=781.25R3125 = 781.25 R R=3125781.25=4% per annumR = 3125781.25=4\displaystyle \frac{3125}{781.25} = 4\%  per annum\displaystyle \text{ per annum} Hence, **Option C** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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If Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

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