Mathematics of FinanceMCQMTP May 18Question 1277 of 512
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The compound interest on a certain sum is $200\displaystyle $209 simple interest is $200for\displaystyle for2$ years. What is the rate per cent for $2$ years?

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

✅ Option a — 9%\displaystyle 9\%

All Options:

  • A9%\displaystyle 9\%
  • B$18\%$
  • C$4.5\%$
  • D$10\%$

Detailed Solution & Explanation

**Derivation of Interest Rate** Given: - Simple Interest (SI\displaystyle SI) for 2\displaystyle 2 years = Rs. 200\displaystyle Rs. \displaystyle \text{Rs. }200 - Compound Interest (CI\displaystyle CI) for 2\displaystyle 2 years = Rs. 209\displaystyle Rs. \displaystyle \text{Rs. }209 **Step 1: Calculate Simple Interest per year** SI1=2002=Rs. 100SI_1 = \displaystyle \frac{200}{2} = \text{Rs. }100 **Step 2: Find the difference between CI and SI** Difference=CI−SI=209−200=Rs. 9\displaystyle \text{Difference} = CI - SI = 209 - 200 = \text{Rs. }9 This difference is the interest earned on the first year's interest of Rs. 100 for 1 year. **Step 3: Solve for the rate of interest (R\displaystyle R)** Difference=SI1×R×1100\displaystyle \text{Difference} = \frac{SI_1 ×\displaystyle \times R ×\displaystyle \times 1}{100} 9=100×R×11009 = 100×R×1100\displaystyle \frac{100 \times R \times 1}{100} 9=R  ⟹  R=9% per annum9 = R \implies R = 9\%  per annum\displaystyle \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

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.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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