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

Options

A63,712\displaystyle 63,712
B65,568\displaystyle 65,568
C53,712\displaystyle 53,712
D41,712\displaystyle 41,712
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Correct Answer

Option b65,568\displaystyle 65,568

All Options:

  • A63,712\displaystyle 63,712
  • B65,568\displaystyle 65,568
  • C53,712\displaystyle 53,712
  • D41,712\displaystyle 41,712

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Detailed Solution & Explanation

Let the present value be PV\displaystyle PV. Given parameters: * Desired Future Value (FV\displaystyle FV) = Rs. 1,50,000\displaystyle \text{Rs. }1,50,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = 18%\displaystyle 18\% p.a. compounded annually, so i=0.18\displaystyle i = 0.18 The formula for present value under compound interest is: PV=FV(1+i)nPV = \frac{FV}{(1+i)^n} Substituting the values: PV=1,50,000(1.18)5PV = \frac{1,50,000}{(1.18)^5} First, let's calculate (1.18)5\displaystyle (1.18)^5: (1.18)52.287758(1.18)^5 \approx 2.287758 Now substitute this back: PV=1,50,0002.28775865,566.7PV = \frac{1,50,000}{2.287758} \approx 65,566.7 The closest option listed is Option B (Rs. 65,568\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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