Mathematics of FinancePYQ Jan 26Question 4256 of 507
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The present value (in nearest ₹) of an annuity of ₹ 90,000 for 13 years at 5.5% compounded annually is (Given 1.055−13=0.4985\displaystyle 1.055^{-13} = 0.4985)

Options

A₹ 9,99,996
B₹ 8,20,548
C₹ 9,69,996
D₹ 7,22,536
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Correct Answer

✅ Option b — ₹ 8,20,548

All Options:

  • A₹ 9,99,996
  • B₹ 8,20,548
  • C₹ 9,69,996
  • D₹ 7,22,536

Detailed Solution & Explanation

The formula for the present value of an ordinary annuity is: PV=A×[1−(1+i)−ni]PV = A \times \left[ \frac{1 - (1 + i)^{-n}}{i} \right] where: - A=₹ 90,000\displaystyle A = \text{₹ } 90,000 (the annual payment) - i=5.5%=0.055\displaystyle i = 5.5\% = 0.055 (the annual interest rate) - n=13\displaystyle n = 13 years (the number of periods)
Using the exact calculation: 1.055−13≈0.49855391.055^{-13} \approx 0.4985539 Substituting the exact value: PV=90,000×[1−0.49855390.055]PV = 90,000 \times \left[ \frac{1 - 0.4985539}{0.055} \right] PV=90,000×[0.50144610.055]PV = 90,000 \times \left[ \frac{0.5014461}{0.055} \right] PV=90,000×9.117202=8,20,548.18≈₹ 8,20,548PV = 90,000 \times 9.117202 = 8,20,548.18 \approx \text{₹ } 8,20,548
If we use the rounded value given in the problem, 1.055−13=0.4985\displaystyle 1.055^{-13} = 0.4985: PV=90,000×[1−0.49850.055]PV = 90,000 \times \left[ \frac{1 - 0.4985}{0.055} \right] PV=90,000×[0.50150.055]=90,000×9.118182=₹ 8,20,636PV = 90,000 \times \left[ \frac{0.5015}{0.055} \right] = 90,000 \times 9.118182 = \text{₹ } 8,20,636 The options are based on the exact value of 1.055−13\displaystyle 1.055^{-13} which gives ₹ 8,20,548. Hence, **Option B** 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.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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