Mathematics of FinanceMCQMTP Mar 22/ RTP Sep 24Question 1351 of 512
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If 10,000\displaystyle 10,000 is invested at 8%\displaystyle 8\% per annum, then compounded quarterly. Then value of investment after 2\displaystyle 2 years is.

Options

A11,716.59\displaystyle 11,716.59
B10,716.59\displaystyle 10,716.59
C12,715.59\displaystyle 12,715.59
Dnone of these
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Correct Answer

Option a11,716.59\displaystyle 11,716.59

All Options:

  • A11,716.59\displaystyle 11,716.59
  • B10,716.59\displaystyle 10,716.59
  • C12,715.59\displaystyle 12,715.59
  • Dnone of these

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Detailed Solution & Explanation

**Derivation of Compound Interest Value** Given: - Principal (P\displaystyle P) = Rs. 10,000\displaystyle \text{Rs. }10,000 - Nominal Rate (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded quarterly - Time (t\displaystyle t) = 2\displaystyle 2 years **Step 1: Calculate periodic rate (i\displaystyle i) and total periods (n\displaystyle n)** - Periodic rate i=r4=8%4=2%=0.02\displaystyle i = \frac{r}{4} = \frac{8\%}{4} = 2\% = 0.02 per quarter. - Total periods n=t×4=2×4=8\displaystyle n = t \times 4 = 2 \times 4 = 8 quarters. **Step 2: Calculate the future value (A\displaystyle A)** A=P(1+i)nA = P(1 + i)^n A=10000(1+0.02)8A = 10000(1 + 0.02)^8 A=10000(1.02)8A = 10000(1.02)^8 Using (1.02)81.171659\displaystyle (1.02)^8 \approx 1.171659: A=10000×1.171659=Rs. 11,716.59A = 10000 \times 1.171659 = \text{Rs. }11,716.59 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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