Mathematics of FinanceMCQPYQ Jun 24Question 1474 of 512
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Find the future value of an annuity of $5,000$ made annually for $6\displaystyle years at rate of $12\% compounded annually, if (1+0.12)6=1.9738\displaystyle (1+0.12)^6 = 1.9738

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

✅ Option c — $39,465$

All Options:

  • A$45,575$
  • B$40,575$
  • C$39,465$
  • D$37,828$

Detailed Solution & Explanation

Let the principal be P\displaystyle P and the compound interest be CI\displaystyle CI. The ratio of the principal to the compound interest for 3\displaystyle 3 years (compounded annually) is given as: PCI=216127PCI=216127\displaystyle \frac{P}{CI} = \frac{216}{127} Let P=216x\displaystyle P = 216x and CI=127x\displaystyle CI = 127x. The total amount A\displaystyle A is: A=P+CI=216x+127x=343xA = P + CI = 216x + 127x = 343x The formula for compound interest amount is: A=P(1+i)3A = P(1+i)^3 where i\displaystyle i is the annual rate of interest. Substituting the values: 343x=216x(1+i)3343x = 216x(1+i)^3 (1+i)3=343216(1+i)^3 = 343216\displaystyle \frac{343}{216} (1+i)3=(76)3(1+i)^3 = \left(76\displaystyle \frac{7}{6}\right)^3 Taking the cube root on both sides: 1+i=761+i = 76\displaystyle \frac{7}{6} i=76−1=16≈0.1666 or 16.66%i = 76−1=16\displaystyle \frac{7}{6} - 1 = \frac{1}{6} ≈\displaystyle \approx 0.1666  or \displaystyle \text{ or } 16.66\% Thus, the rate of interest is approximately $0.1666$. 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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