Mathematics of FinanceMCQMTP Jun 23 Series IIQuestion 1387 of 512
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If the compound interest on a certain sum of money for 2\displaystyle 2 years at 5%\displaystyle 5\% p.a. be $50.44$, then the simple interest (S.I.) is

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

✅ Option c — $48$

All Options:

  • A$50$
  • B$49$
  • C$48$
  • DNone of these

Detailed Solution & Explanation

**Derivation of Simple Interest** Given: - Compound Interest (CI\displaystyle CI) = Rs. 50.44\displaystyle Rs. \displaystyle \text{Rs. }50.44 - Time (t\displaystyle t) = 2\displaystyle 2 years - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum **Step 1: Express compound interest in terms of principal P\displaystyle P** CI=P[(1+r)2−1]CI = P \left[ (1 + r)^2 - 1 \right] 50.44=P[(1.05)2−1]50.44 = P \left[ (1.05)^2 - 1 \right] 50.44=P[1.1025−1]50.44 = P [ 1.1025 - 1 ] 50.44=0.1025P50.44 = 0.1025 P P=50.440.1025≈Rs. 492.10P = 50.440.1025\displaystyle \frac{50.44}{0.1025} ≈\displaystyle \approx Rs. \displaystyle \text{Rs. }492.10 **Step 2: Calculate Simple Interest (SI\displaystyle SI) on the same principal** SI=P×R×t100SI = P×R×t100\displaystyle \frac{P \times R \times t}{100} SI=492.10×5×2100=492.10×0.10≈Rs. 49.21SI = 492.10×5×2100=492\displaystyle \frac{492.10 \times 5 \times 2}{100} = 492.10 ×\displaystyle \times 0.10 ≈\displaystyle \approx Rs. \displaystyle \text{Rs. }49.21 *(Note: Option B ($49$) is mathematically correct. The database lists Option C ($48$) as correct, which is a typo in the key. We note that 49 is the correct choice.)* 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.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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