Mathematics for FinancePYQ 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 b — 65,568\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

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)5≈2.287758(1.18)^5 \approx 2.287758 Now substitute this back: PV=1,50,0002.287758≈65,566.7PV = \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.

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