Mathematics for FinanceMTP Dec 23 Series IQuestion 1421 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

Given parameters: * Nominal annual interest rate (r\displaystyle r) = 9.9%\displaystyle 9.9\% p.a. =0.099\displaystyle = 0.099 * Compounding frequency (m\displaystyle m) = 12\displaystyle 12 (compounded monthly) The monthly interest rate (i\displaystyle i) is: i=rm=0.09912=0.00825i = \frac{r}{m} = \frac{0.099}{12} = 0.00825 The formula for the effective annual rate of interest (E\displaystyle E) is: E=(1+i)m−1E = (1 + i)^m - 1 Substituting the values: E=(1+0.00825)12−1E = (1 + 0.00825)^{12} - 1 E=(1.00825)12−1E = (1.00825)^{12} - 1 Let's compute (1.00825)12\displaystyle (1.00825)^{12} step-by-step: (1.00825)2≈1.016568(1.00825)^2 \approx 1.016568 (1.00825)4≈1.033411(1.00825)^4 \approx 1.033411 (1.00825)8≈1.067937(1.00825)^8 \approx 1.067937 (1.00825)12=(1.00825)8×(1.00825)4≈1.067937×1.033411≈1.103622(1.00825)^{12} = (1.00825)^8 \times (1.00825)^4 \approx 1.067937 \times 1.033411 \approx 1.103622 Thus: E≈1.103622−1=0.103622=10.36%E \approx 1.103622 - 1 = 0.103622 = 10.36\% The effective annual rate of interest is 10.36%\displaystyle 10.36\%. Hence, **Option A** is the correct answer.

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