Mathematics of FinancePYQ Jan 26Question 4554 of 507
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The value of compound interest (in nearest ₹) if ₹ 30,00,000 is deposited in a bank for 1 year at the rate of 16% per annum compounded quarterly is:

Options

A₹ 5,07,575
B₹ 5,78,360
C₹ 5,09,576
D₹ 5,72,540
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Correct Answer

Option c₹ 5,09,576

All Options:

  • A₹ 5,07,575
  • B₹ 5,78,360
  • C₹ 5,09,576
  • D₹ 5,72,540

Detailed Solution & Explanation

The formula for the accumulated amount under quarterly compounding is: A=P(1+r400)4tA = P \left(1 + \frac{r}{400}\right)^{4t} where: - P=₹ 30,00,000\displaystyle P = \text{₹ } 30,00,000 is the principal amount - r=16%\displaystyle r = 16\% is the nominal annual rate of interest - t=1 year\displaystyle t = 1\text{ year} is the time duration - The number of compounding periods in a year is 4\displaystyle 4 (quarterly)
Substituting these values: A=30,00,000(1+16400)4×1A = 30,00,000 \left(1 + \frac{16}{400}\right)^{4 \times 1} A=30,00,000(1.04)4A = 30,00,000 (1.04)^4
First, let us compute (1.04)4\displaystyle (1.04)^4: (1.04)2=1.0816(1.04)^2 = 1.0816 (1.04)4=(1.0816)2=1.16985856(1.04)^4 = (1.0816)^2 = 1.16985856
Now, calculate the accumulated amount A\displaystyle A: A=30,00,000×1.16985856=35,09,575.68A = 30,00,000 \times 1.16985856 = 35,09,575.68
The compound interest is given by: CI=APCI = A - P CI=35,09,575.6830,00,000=5,09,575.68₹ 5,09,576CI = 35,09,575.68 - 30,00,000 = 5,09,575.68 \approx \text{₹ } 5,09,576 Hence, **Option C** 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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