Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1429 of 512
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A person gave a loan of 200\displaystyle 200 to Mr. X and recovered it at the rate of 35\displaystyle 35 for eight months, commencing from the end of first month. What is the effective rate of simple interest?

Options

A10%\displaystyle 10\%
B20%\displaystyle 20\%
C40%\displaystyle 40\%
D60%\displaystyle 60\%
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Correct Answer

Option d60%\displaystyle 60\%

All Options:

  • A10%\displaystyle 10\%
  • B20%\displaystyle 20\%
  • C40%\displaystyle 40\%
  • D60%\displaystyle 60\%

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Detailed Solution & Explanation

Given parameters: * Loan Amount (Principal, P\displaystyle P) = Rs. 200\displaystyle \text{Rs. }200 * Monthly Installment (x\displaystyle x) = Rs. 35\displaystyle \text{Rs. }35 * Number of months (n\displaystyle n) = 8\displaystyle 8 Total amount recovered = 35×8=Rs. 280\displaystyle 35 \times 8 = \text{Rs. }280. Total interest charged = 280200=Rs. 80\displaystyle 280 - 200 = \text{Rs. }80. Since payments are made monthly, the interest is calculated on a reducing balance basis or by the formula for simple interest on installments: I=nxPP×12nI = \frac{n \cdot x - P}{P} \times \frac{12}{n} Using the flat simple interest rate: I=P×R×t    80=200×R×812    80=4003R    R=240400=60% p.a.I = P \times R \times t \implies 80 = 200 \times R \times \frac{8}{12} \implies 80 = \frac{400}{3} R \implies R = \frac{240}{400} = 60\% \text{ p.a.} Thus, the effective rate of simple interest is 60%\displaystyle 60\% per annum. Hence, **Option D** 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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