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

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

✅ Option b — 5%\displaystyle 5\%

All Options:

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

Detailed Solution & Explanation

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Interest} = I_1 + I_2 = 380 R **Step 2: Determine total interest earned from cash flows** The total money received/withdrawn by the person is $4,000 + 7,900 = Rs.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

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.

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