Mathematics of FinanceMCQMTP May 19Question 1495 of 512
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Suppose your father decides to gift you $10,000\displaystyle every year starting from today for the next five years, you deposit this amount in a bank as and when you receive and get $10\% p.a. C.I. What is the present value of this annuity?

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

✅ Option b — $64,698.70$

All Options:

  • A$65,156$
  • B$64,698.70$
  • C$41,698.70$
  • DNone

Detailed Solution & Explanation

Since payments start today, this is an annuity due. The present value (PVdue\displaystyle PV_{due\displaystyle \text{due}}) is: PVdue=A+A×P(4,0.10)PV_{due\displaystyle \text{due}} = A + A ×\displaystyle \times P(4, 0.10) Given: * Annual payment (A\displaystyle A) = $10,000$ * Factor P(4,0.10)=3.16987\displaystyle P(4, 0.10) = 3.16987 Substituting the values: PVdue=10,000+10,000×3.16987=41,698.70PV_{due\displaystyle \text{due}} = 10,000 + 10,000 ×\displaystyle \times 3.16987 = 41,698.70 Mathematically, this is Option C ($41,698.70$). However, the official key marks Option B ($64,698.70$). 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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