Mathematics of FinanceMCQPYQ Nov 18Question 1177 of 512
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If an amount is kept at S. I. it earns an interest of Rs. 600\displaystyle \text{Rs. }600 in first two years but when kept at compound interest it earns an interest of Rs. 660\displaystyle \text{Rs. }660 for the same period, then the rate of interest and principal amount respectively are:

Options

A20%,Rs. 1,200\displaystyle 20\%, \text{Rs. }1,200
B20%,Rs. 1,500\displaystyle 20\%, \text{Rs. }1,500
C10%,Rs. 1,200\displaystyle 10\%, \text{Rs. }1,200
D10%,Rs. 1,500\displaystyle 10\%, \text{Rs. }1,500
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Correct Answer

Option b20%,Rs. 1,500\displaystyle 20\%, \text{Rs. }1,500

All Options:

  • A20%,Rs. 1,200\displaystyle 20\%, \text{Rs. }1,200
  • B20%,Rs. 1,500\displaystyle 20\%, \text{Rs. }1,500
  • C10%,Rs. 1,200\displaystyle 10\%, \text{Rs. }1,200
  • D10%,Rs. 1,500\displaystyle 10\%, \text{Rs. }1,500

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Detailed Solution & Explanation

**Derivation of Rate and Principal from Simple and Compound Interest** Given: - Simple Interest (SI\displaystyle SI) for 2\displaystyle 2 years = Rs. 600\displaystyle \text{Rs. }600 - Compound Interest (CI\displaystyle CI) for 2\displaystyle 2 years = Rs. 660\displaystyle \text{Rs. }660 **Step 1: Find Simple Interest for 1\displaystyle 1 year** Since Simple Interest is constant every year: SI for 1st year=6002=Rs. 300\text{SI for 1st year} = \frac{600}{2} = \text{Rs. }300 SI for 2nd year=Rs. 300\text{SI for 2nd year} = \text{Rs. }300 **Step 2: Determine the difference between CI and SI** For the first year, SI=CI=Rs. 300\displaystyle SI = CI = \text{Rs. }300. The difference in the interest in the second year is due to the interest earned on the first year's interest. Difference=CISI=660600=Rs. 60\text{Difference} = CI - SI = 660 - 600 = \text{Rs. }60 This Rs. 60\displaystyle \text{Rs. }60 is the interest earned on Rs. 300\displaystyle \text{Rs. }300 (the first year's interest) for 1\displaystyle 1 year. **Step 3: Calculate the Rate of Interest (R\displaystyle R)** Interest=Principal×R×T100\text{Interest} = \frac{\text{Principal} \times R \times T}{100} 60=300×R×110060 = \frac{300 \times R \times 1}{100} 60=3R    R=20% per annum60 = 3R \implies R = 20\% \text{ per annum} **Step 4: Calculate the Principal Amount (P\displaystyle P)** Using the Simple Interest of the first year: SI for 1st year=P×R×1100\text{SI for 1st year} = \frac{P \times R \times 1}{100} 300=P×20×1100300 = \frac{P \times 20 \times 1}{100} 300=P5    P=Rs. 1,500300 = \frac{P}{5} \implies P = \text{Rs. }1,500 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.

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