Mathematics for FinanceMTP 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 d — 60%\displaystyle 60\%

All Options:

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

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 = 280−200=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=n⋅x−PP×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.

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