Mathematics of FinanceMCQMTP 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 b4%\displaystyle 4\%

All Options:

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

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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=AP=5000046875=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.

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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