Mathematics of FinanceMCQPYQ July 21Question 1448 of 512
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If the desired future value after 5\displaystyle 5 years with $18\%$ interest rate is $₹ 1,50,000$, then the present value (in $₹$) is

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

✅ Option b — $65,568$

All Options:

  • A$63,712$
  • B$65,568$
  • C$53,712$
  • D$41,712$

Detailed Solution & Explanation

Let the present value be PV\displaystyle PV. Given parameters: * Desired Future Value (FV\displaystyle FV) = Rs. 1,50,000\displaystyle Rs. \displaystyle \text{Rs. }1,50,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = $18\%$ p.a. compounded annually, so $i = 0.18$ The formula for present value under compound interest is: PV=FV(1+i)nPV = FV(1+i)n\displaystyle \frac{FV}{(1+i)^n} Substituting the values: PV=1,50,000(1.18)5PV = 1,50,000(1.18)5\displaystyle \frac{1,50,000}{(1.18)^5} First, let's calculate (1.18)5\displaystyle (1.18)^5: (1.18)5≈2.287758(1.18)^5 ≈\displaystyle \approx 2.287758 Now substitute this back: PV=1,50,0002.287758≈65,566.7PV = 1,50,0002.287758\displaystyle \frac{1,50,000}{2.287758} ≈\displaystyle \approx 65,566.7 The closest option listed is Option B (Rs. 65,568\displaystyle Rs. \displaystyle \text{Rs. }65,568). 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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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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If Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

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