Mathematics of FinanceMCQPYQ Dec 23Question 1467 of 512
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Govinda's mother decides to gift him 50,000\displaystyle 50,000 every year starting from today for the next five years. Govinda deposits this amount in a bank as and when he receives and gets 10%\displaystyle 10\% per annum interest rate, compounded annually. What is the present value of this annuity? Given P(4,0.10)=3.16987\displaystyle P(4,0.10) = 3.16987.

Options

A2,80,493.5\displaystyle 2,80,493.5
B2,08,493.5\displaystyle 2,08,493.5
C2,08,943.5\displaystyle 2,08,943.5
D2,58,493.5\displaystyle 2,58,493.5
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Correct Answer

Option a2,80,493.5\displaystyle 2,80,493.5

All Options:

  • A2,80,493.5\displaystyle 2,80,493.5
  • B2,08,493.5\displaystyle 2,08,493.5
  • C2,08,943.5\displaystyle 2,08,943.5
  • D2,58,493.5\displaystyle 2,58,493.5

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Detailed Solution & Explanation

Let the principal amount be P\displaystyle P. The rate of interest is r=5%\displaystyle r = 5\% p.a., so i=5100=0.05\displaystyle i = \frac{5}{100} = 0.05. The time period is t=2\displaystyle t = 2 years. The formula for the difference between Compound Interest (CI\displaystyle CI) and Simple Interest (SI\displaystyle SI) for a 2\displaystyle 2-year period is: CISI=P×i2CI - SI = P \times i^2 Given that the difference is Rs. 21\displaystyle \text{Rs. }21: 21=P×(0.05)221 = P \times (0.05)^2 21=P×0.002521 = P \times 0.0025 Solving for P\displaystyle P: P=210.0025=8,400P = \frac{21}{0.0025} = 8,400 Thus, the principal amount is Rs. 8,400\displaystyle \text{Rs. }8,400. (Note: While some keys mark Option D, the mathematically correct value is Option A). Hence, **Option A** 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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