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

Options

A45,575\displaystyle 45,575
B40,575\displaystyle 40,575
C39,465\displaystyle 39,465
D37,828\displaystyle 37,828
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Correct Answer

Option c39,465\displaystyle 39,465

All Options:

  • A45,575\displaystyle 45,575
  • B40,575\displaystyle 40,575
  • C39,465\displaystyle 39,465
  • D37,828\displaystyle 37,828

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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=216127\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 = \frac{343}{216} (1+i)3=(76)3(1+i)^3 = \left(\frac{7}{6}\right)^3 Taking the cube root on both sides: 1+i=761+i = \frac{7}{6} i=761=160.1666 or 16.66%i = \frac{7}{6} - 1 = \frac{1}{6} \approx 0.1666 \text{ or } 16.66\% Thus, the rate of interest is approximately 0.1666\displaystyle 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

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