Mathematics of FinanceMCQMTP Nov 18Question 1272 of 512
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A lent 6000\displaystyle 6000 to B for 2\displaystyle 2 years and 1500\displaystyle 1500 to C for 4\displaystyle 4 years and received total interest of 900\displaystyle 900 from both. The rate of interest when simple interest method calculated.

Options

A5%\displaystyle 5\%
B6%\displaystyle 6\%
C7.5%\displaystyle 7.5\%
D9%\displaystyle 9\%
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Correct Answer

Option a5%\displaystyle 5\%

All Options:

  • A5%\displaystyle 5\%
  • B6%\displaystyle 6\%
  • C7.5%\displaystyle 7.5\%
  • D9%\displaystyle 9\%

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Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Sum 1 lent to B (P1\displaystyle P_1) = Rs. 6,000\displaystyle \text{Rs. }6,000 for t1=2\displaystyle t_1 = 2 years - Sum 2 lent to C (P2\displaystyle P_2) = Rs. 1,500\displaystyle \text{Rs. }1,500 for t2=4\displaystyle t_2 = 4 years - Total interest received from both B and C = Rs. 900\displaystyle \text{Rs. }900 **Step 1: Set up the Simple Interest equations** Total Interest=SIB+SIC\text{Total Interest} = SI_B + SI_C 900=6000×R×2100+1500×R×4100900 = \frac{6000 \times R \times 2}{100} + \frac{1500 \times R \times 4}{100} 900=120R+60R900 = 120 R + 60 R 900=180R900 = 180 R **Step 2: Solve for R\displaystyle R** R=900180=5% per annumR = \frac{900}{180} = 5\% \text{ per annum} Hence, **Option A** 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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