Mathematics of FinanceMCQPYQ Nov 19Question 1294 of 512
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A person deposited a sum of 10,000\displaystyle 10,000 in a bank. After 2\displaystyle 2 years, he withdrew 4,000\displaystyle 4,000 and at the end of 5\displaystyle 5 years, he received an amount of 7,900\displaystyle 7,900; then the rate of simple interest is:

Options

A6%\displaystyle 6\%
B5%\displaystyle 5\%
C10%\displaystyle 10\%
DNone of these
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Correct Answer

Option b5%\displaystyle 5\%

All Options:

  • A6%\displaystyle 6\%
  • B5%\displaystyle 5\%
  • C10%\displaystyle 10\%
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Initial Principal (P\displaystyle P) = Rs. 10,000\displaystyle \text{Rs. }10,000 - At t=2\displaystyle t=2 years, withdrawal = Rs. 4,000\displaystyle \text{Rs. }4,000, leaving a new principal of Rs. 6,000\displaystyle \text{Rs. }6,000 for the remaining 3\displaystyle 3 years. - Total amount received at t=5\displaystyle t=5 years = Rs. 7,900\displaystyle \text{Rs. }7,900 **Step 1: Set up interest equations for both periods** - Interest for first 2 years: I1=10000×R×2100=200RI_1 = \frac{10000 \times R \times 2}{100} = 200 R - Interest for the remaining 3 years: I2=6000×R×3100=180RI_2 = \frac{6000 \times R \times 3}{100} = 180 R - Total simple interest earned over 5 years: Total Interest=I1+I2=380R\text{Total Interest} = I_1 + I_2 = 380 R **Step 2: Determine total interest earned from cash flows** The total money received/withdrawn by the person is 4,000+7,900=Rs. 11,900\displaystyle 4,000 + 7,900 = \text{Rs. }11,900. Since the initial deposit was 10,000\displaystyle 10,000: Total Interest Earned=1190010000=Rs. 1,900\text{Total Interest Earned} = 11900 - 10000 = \text{Rs. }1,900 **Step 3: Solve for Rate (R\displaystyle R)** 380R=1900380 R = 1900 R=1900380=5% per annumR = \frac{1900}{380} = 5\% \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

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