Mathematics of FinanceMCQPYQ Nov. 20Question 1440 of 512
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Find the present value of 1,00,000\displaystyle ₹ 1,00,000 to be required after 5\displaystyle 5 years if the interest rate be 9%\displaystyle 9\%. Given that (1.09)5=1.5386\displaystyle (1.09)^5 = 1.5386.

Options

A70,993.48\displaystyle 70,993.48
B64,994.15\displaystyle 64,994.15
C88,992.43\displaystyle 88,992.43
D93,902.12\displaystyle 93,902.12
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Correct Answer

Option b64,994.15\displaystyle 64,994.15

All Options:

  • A70,993.48\displaystyle 70,993.48
  • B64,994.15\displaystyle 64,994.15
  • C88,992.43\displaystyle 88,992.43
  • D93,902.12\displaystyle 93,902.12

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Detailed Solution & Explanation

Let the present value (the amount to be invested today) be PV\displaystyle PV. Given parameters: * Future Value (FV\displaystyle FV) = Rs. 1,00,000\displaystyle \text{Rs. }1,00,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = 9%\displaystyle 9\% p.a., so i=0.09\displaystyle i = 0.09 * Given factor: (1.09)5=1.5386\displaystyle (1.09)^5 = 1.5386 The compound interest amount formula is: FV=PV×(1+i)nFV = PV \times (1+i)^n Substituting the values: 1,00,000=PV×(1.09)51,00,000 = PV \times (1.09)^5 1,00,000=PV×1.53861,00,000 = PV \times 1.5386 Solving for PV\displaystyle PV: PV=1,00,0001.538664,994.15PV = \frac{1,00,000}{1.5386} \approx 64,994.15 Thus, the present value is approximately Rs. 64,994.15\displaystyle \text{Rs. }64,994.15. 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

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