Mathematics of FinanceMCQMTP 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 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

**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)121E = (1 + i)^{12} - 1 E=(1+0.00825)121E = (1 + 0.00825)^{12} - 1 E=(1.00825)121E = (1.00825)^{12} - 1 E1.1036221=0.103622 or 10.36%E \approx 1.103622 - 1 = 0.103622 \text{ or } 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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