Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 1527 of 512
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A debt of $5000$ with interest at the rate of $8\%$ compounded quarterly is to be discharged by $8$ equal quarterly payments, the first payment being due today. Find the size of each payment.

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

✅ Option b — $669.11$

All Options:

  • A$673.90$
  • B$669.11$
  • C$399.26$
  • DNone of these

Detailed Solution & Explanation

Since the first payment is due today, this is an annuity due. The present value (PVdue\displaystyle PV_{due\displaystyle \text{due}}) is: PVdue=A[1+1−(1+i)−(n−1)i]PV_{due\displaystyle \text{due}} = A \left[ 1 + 1−(1+i)−(n−1)i\displaystyle \frac{1 - (1+i)^{-(n-1)}}{i} \right] Given: * Loan amount (PVdue\displaystyle PV_{due\displaystyle \text{due}}) = $5,000$ * Number of periods (n\displaystyle n) = 8\displaystyle 8 * Nominal rate = 8%\displaystyle 8\% p.a. compounded quarterly, so periodic rate i=8%4=2%=0.02\displaystyle i = 8%4=2\displaystyle \frac{8\%}{4} = 2\% = 0.02 Substituting the values: 5,000=A[1+1−(1.02)−70.02]5,000 = A \left[ 1 + 1−(1.02)−70.02\displaystyle \frac{1 - (1.02)^{-7}}{0.02} \right] Using (1.02)−7≈0.87056\displaystyle (1.02)^{-7} ≈\displaystyle \approx 0.87056: 5,000=A[1+6.47199]=A×7.471995,000 = A [ 1 + 6.47199 ] = A ×\displaystyle \times 7.47199 A=5,0007.47199≈669.17A = 5,0007.47199\displaystyle \frac{5,000}{7.47199} ≈\displaystyle \approx 669.17 This is closest to Option B ($669.11$). 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.

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