Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 1401 of 512
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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Options

A4,000\displaystyle 4,000
B5,000\displaystyle 5,000
C6,000\displaystyle 6,000
DNone of these
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Correct Answer

Option b5,000\displaystyle 5,000

All Options:

  • A4,000\displaystyle 4,000
  • B5,000\displaystyle 5,000
  • C6,000\displaystyle 6,000
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Principal Sum** Given: - Time (t\displaystyle t) = 2.5\displaystyle 2.5 years - Let the original rate be R\displaystyle R. - If rate increases by 4%\displaystyle 4\%, interest increases by Rs. 500\displaystyle \text{Rs. }500. **Step 1: Express the interest difference** Interest Difference=P×(R+4)×t100P×R×t100\text{Interest Difference} = \frac{P \times (R + 4) \times t}{100} - \frac{P \times R \times t}{100} 500=P×4×t100500 = \frac{P \times 4 \times t}{100} 500=P×4×2.5100500 = \frac{P \times 4 \times 2.5}{100} 500=10P100500 = \frac{10 P}{100} 500=0.10P500 = 0.10 P **Step 2: Solve for P\displaystyle P** P=5000.10=Rs. 5,000P = \frac{500}{0.10} = \text{Rs. }5,000 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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