Mathematics of FinanceMCQMTP Jun 23 Series IQuestion 1518 of 512
All Questions

Find the present value of an ordinary annuity of 8\displaystyle 8 quarterly payments of 500\displaystyle 500 each, the rate of interest being 8%\displaystyle 8\% p.a. compounded quarterly

Options

A3270.00\displaystyle 3270.00
B4725.00\displaystyle 4725.00
C3662.50\displaystyle 3662.50
D3266.50\displaystyle 3266.50
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option c3662.50\displaystyle 3662.50

All Options:

  • A3270.00\displaystyle 3270.00
  • B4725.00\displaystyle 4725.00
  • C3662.50\displaystyle 3662.50
  • D3266.50\displaystyle 3266.50

Ad

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of an ordinary annuity compounded quarterly is: PV=A×[1(1+i)ni]PV = A \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Quarterly payment (A\displaystyle A) = 500\displaystyle 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 = \frac{8\%}{4} = 2\% = 0.02 Substituting the values: PV=500×[1(1.02)80.02]PV = 500 \times \left[ \frac{1 - (1.02)^{-8}}{0.02} \right] Using (1.02)80.85349\displaystyle (1.02)^{-8} \approx 0.85349: PV=500×[10.853490.02]=500×7.325483,662.74PV = 500 \times \left[ \frac{1 - 0.85349}{0.02} \right] = 500 \times 7.32548 \approx 3,662.74 This is closest to Option C (3662.50\displaystyle 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

Related Comparison Tables

More Questions from Mathematics of Finance

Ready to Master Mathematics of Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free