Mathematics for FinanceMTP Nov 21Question 1331 of 512
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Arun purchased a vacuum cleaner by giving 1700\displaystyle 1700 as cash down payment, which will be followed by five EMIs of 480\displaystyle 480 each. The vacuum cleaner can also be bought by paying 3900\displaystyle 3900 cash. What is the approx. rate of interest p.a. (at simple interest) under this instalment plan?

Options

A18%\displaystyle 18\%
B19%\displaystyle 19\%
C22%\displaystyle 22\%
D20%\displaystyle 20\%
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Correct Answer

✅ Option c — 22%\displaystyle 22\%

All Options:

  • A18%\displaystyle 18\%
  • B19%\displaystyle 19\%
  • C22%\displaystyle 22\%
  • D20%\displaystyle 20\%

Detailed Solution & Explanation

**Derivation of Approximate Simple Interest Rate under Instalment Plan** Given: - Cash Price = Rs. 3,900\displaystyle \text{Rs. }3,900 - Down Payment = Rs. 1,700\displaystyle \text{Rs. }1,700 - Principal borrowed (P\displaystyle P) = 3900−1700=Rs. 2,200\displaystyle 3900 - 1700 = \text{Rs. }2,200 - Five monthly instalments of Rs. 480\displaystyle \text{Rs. }480 each - Total amount paid via EMIs = 5×480=Rs. 2,400\displaystyle 5 \times 480 = \text{Rs. }2,400 - Total Simple Interest paid (SI\displaystyle SI) = 2400−2200=Rs. 200\displaystyle 2400 - 2200 = \text{Rs. }200 - Total period (T\displaystyle T) = 5\displaystyle 5 months = 512\displaystyle \frac{5}{12} year **Step 1: Apply the standard simple interest formula as a textbook approximation** Using SI=P×R×T100\displaystyle SI = \frac{P \times R \times T}{100}: 200=2200×R×512100200 = \frac{2200 \times R \times \frac{5}{12}}{100} 200=22×R×512200 = 22 \times R \times \frac{5}{12} 200=R×11012200 = R \times \frac{110}{12} R=2400110=21.82%≈22% per annumR = \frac{2400}{110} = 21.82\% \approx 22\% \text{ per annum} Hence, **Option C** is the correct answer.

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