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\displaystyle 50.44, then the simple interest (S.I.) is

Options

A50\displaystyle 50
B49\displaystyle 49
C48\displaystyle 48
DNone of these
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Correct Answer

Option c48\displaystyle 48

All Options:

  • A50\displaystyle 50
  • B49\displaystyle 49
  • C48\displaystyle 48
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Simple Interest** Given: - Compound Interest (CI\displaystyle CI) = Rs. 50.44\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)21]CI = P \left[ (1 + r)^2 - 1 \right] 50.44=P[(1.05)21]50.44 = P \left[ (1.05)^2 - 1 \right] 50.44=P[1.10251]50.44 = P [ 1.1025 - 1 ] 50.44=0.1025P50.44 = 0.1025 P P=50.440.1025Rs. 492.10P = \frac{50.44}{0.1025} \approx \text{Rs. }492.10 **Step 2: Calculate Simple Interest (SI\displaystyle SI) on the same principal** SI=P×R×t100SI = \frac{P \times R \times t}{100} SI=492.10×5×2100=492.10×0.10Rs. 49.21SI = \frac{492.10 \times 5 \times 2}{100} = 492.10 \times 0.10 \approx \text{Rs. }49.21 *(Note: Option B (49\displaystyle 49) is mathematically correct. The database lists Option C (48\displaystyle 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

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