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

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

✅ Option d — $60\%$

All Options:

  • A$10\%$
  • B$20\%$
  • C$40\%$
  • D$60\%$

Detailed Solution & Explanation

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

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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