Mathematics of FinanceMCQMTP Jun 23 Series IQuestion 1518 of 512
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Find the present value of an ordinary annuity of 8\displaystyle 8 quarterly payments of $500$ each, the rate of interest being $8\%$ p.a. compounded quarterly

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $3662.50$

All Options:

  • A$3270.00$
  • B$4725.00$
  • C$3662.50$
  • D$3266.50$

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of an ordinary annuity compounded quarterly is: PV=A×[1−(1+i)−ni]PV = A ×\displaystyle \times \left[ 1−(1+i)−ni\displaystyle \frac{1 - (1+i)^{-n}}{i} \right] Given: * Quarterly payment (A\displaystyle A) = $500$ * Number of payments (n\displaystyle n) = 8\displaystyle 8 * Nominal rate = 8%\displaystyle 8\% p.a., so periodic rate i=8%4=2%=0.02\displaystyle i = 8%4=2\displaystyle \frac{8\%}{4} = 2\% = 0.02 Substituting the values: PV=500×[1−(1.02)−80.02]PV = 500 ×\displaystyle \times \left[ 1−(1.02)−80.02\displaystyle \frac{1 - (1.02)^{-8}}{0.02} \right] Using (1.02)−8≈0.85349\displaystyle (1.02)^{-8} ≈\displaystyle \approx 0.85349: PV=500×[1−0.853490.02]=500×7.32548≈3,662.74PV = 500 ×\displaystyle \times \left[ 1−0.853490.02\displaystyle \frac{1 - 0.85349}{0.02} \right] = 500 ×\displaystyle \times 7.32548 ≈\displaystyle \approx 3,662.74 This is closest to Option C ($3662.50$). 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

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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