Mathematics of FinanceMCQPYQ Dec 23Question 1470 of 512
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What will be the future value of an annuity of 2,500\displaystyle 2,500 made annually for 12\displaystyle 12 years at interest rate of 5%\displaystyle 5\% compounded annually

Options

A37,588.58\displaystyle 37,588.58
B39,790.00\displaystyle 39,790.00
C40,873.13\displaystyle 40,873.13
D42,603.68\displaystyle 42,603.68
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Correct Answer

Option a37,588.58\displaystyle 37,588.58

All Options:

  • A37,588.58\displaystyle 37,588.58
  • B39,790.00\displaystyle 39,790.00
  • C40,873.13\displaystyle 40,873.13
  • D42,603.68\displaystyle 42,603.68

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Detailed Solution & Explanation

Let the principal sum be P\displaystyle P. Given parameters: * Final Amount (A\displaystyle A) = Rs. 1,20,000\displaystyle \text{Rs. }1,20,000 * Nominal Interest Rate (r\displaystyle r) = 4%\displaystyle 4\% p.a. * Compounding Frequency (m\displaystyle m) = 2\displaystyle 2 (compounded semi-annually) * Semi-annual Interest Rate (i\displaystyle i) = 4%2=2%=0.02\displaystyle \frac{4\%}{2} = 2\% = 0.02 * Time (t\displaystyle t) = 1\displaystyle 1 year, so number of periods n=1×2=2\displaystyle n = 1 \times 2 = 2 semi-annual periods The formula for compound amount is: A=P(1+i)nA = P(1+i)^n Substituting the values: 1,20,000=P(1.02)21,20,000 = P(1.02)^2 1,20,000=P×1.04041,20,000 = P \times 1.0404 Solving for P\displaystyle P: P=1,20,0001.04041,15,340.25P = \frac{1,20,000}{1.0404} \approx 1,15,340.25 Thus, the principal sum is approximately Rs. 1,15,340\displaystyle \text{Rs. }1,15,340. 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

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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