Mathematics of FinanceMCQMTP 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 a10.36%\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\%

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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)m1E = (1 + i)^m - 1 Substituting the values: E=(1+0.00825)121E = (1 + 0.00825)^{12} - 1 E=(1.00825)121E = (1.00825)^{12} - 1 Let's compute (1.00825)12\displaystyle (1.00825)^{12} step-by-step: (1.00825)21.016568(1.00825)^2 \approx 1.016568 (1.00825)41.033411(1.00825)^4 \approx 1.033411 (1.00825)81.067937(1.00825)^8 \approx 1.067937 (1.00825)12=(1.00825)8×(1.00825)41.067937×1.0334111.103622(1.00825)^{12} = (1.00825)^8 \times (1.00825)^4 \approx 1.067937 \times 1.033411 \approx 1.103622 Thus: E1.1036221=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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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