Mathematics for FinancePYQ June 24Question 1260 of 512
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If the interest rate on a loan is 1%\displaystyle 1\% per month, the effective annual rate of interest is:

Options

A12%\displaystyle 12\%
B12.36%\displaystyle 12.36\%
C12.68%\displaystyle 12.68\%
D12.98%\displaystyle 12.98\%
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Correct Answer

✅ Option c — 12.68%\displaystyle 12.68\%

All Options:

  • A12%\displaystyle 12\%
  • B12.36%\displaystyle 12.36\%
  • C12.68%\displaystyle 12.68\%
  • D12.98%\displaystyle 12.98\%

Detailed Solution & Explanation

**Derivation of Effective Annual Rate** Given: - Monthly interest rate (i\displaystyle i) = 1%=0.01\displaystyle 1\% = 0.01 - Number of periods in a year (m\displaystyle m) = 12\displaystyle 12 **Step 1: Calculate the effective annual rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.01)12−1E = (1 + 0.01)^{12} - 1 E=(1.01)12−1E = (1.01)^{12} - 1 **Step 2: Compute the value** (1.01)12≈1.126825(1.01)^{12} \approx 1.126825 E=1.126825−1=0.126825 or 12.68%E = 1.126825 - 1 = 0.126825 \text{ or } 12.68\% Hence, **Option C** is the correct answer.

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