Mathematics for FinanceMTP Dec 23 Series IQuestion 1396 of 512
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Nominal Rate of Interest is 9.9%\displaystyle 9.9\% p.a. If Interest is compounded monthly, what will be effective rate of Interest.

Options

A10.36%\displaystyle 10.36\%
B9.36%\displaystyle 9.36\%
C11.36%\displaystyle 11.36\%
D9.9%\displaystyle 9.9\%
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Correct Answer

✅ Option a — 10.36%\displaystyle 10.36\%

All Options:

  • A10.36%\displaystyle 10.36\%
  • B9.36%\displaystyle 9.36\%
  • C11.36%\displaystyle 11.36\%
  • D9.9%\displaystyle 9.9\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal rate (r\displaystyle r) = 9.9%\displaystyle 9.9\% per annum compounded monthly **Step 1: Find the monthly interest rate (i\displaystyle i)** i=r12=9.9%12=0.825%=0.00825 per monthi = \frac{r}{12} = \frac{9.9\%}{12} = 0.825\% = 0.00825 \text{ per month} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)12−1E = (1 + i)^{12} - 1 E=(1+0.00825)12−1E = (1 + 0.00825)^{12} - 1 E=(1.00825)12−1E = (1.00825)^{12} - 1 E≈1.103622−1=0.103622 or 10.36%E \approx 1.103622 - 1 = 0.103622 \text{ or } 10.36\% Hence, **Option A** is the correct answer.

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