Mathematics for FinancePYQ June 19Question 1545 of 512
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What is the net present value of piece of property which would be valued at 2\displaystyle 2 lakh at the end of 2\displaystyle 2 years? (Annual rate of increase =5%\displaystyle = 5\%)

Options

A1.81\displaystyle 1.81 lakh
B2.01\displaystyle 2.01 lakh
C2.00\displaystyle 2.00 lakh
DNone of these
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Correct Answer

✅ Option a — 1.81\displaystyle 1.81 lakh

All Options:

  • A1.81\displaystyle 1.81 lakh
  • B2.01\displaystyle 2.01 lakh
  • C2.00\displaystyle 2.00 lakh
  • DNone of these

Detailed Solution & Explanation

The net present value (NPV\displaystyle NPV) of the property is its future value discounted back to the present: PV=FV(1+i)nPV = \frac{FV}{(1+i)^n} Given: * Future Value (FV\displaystyle FV) = 2,00,000\displaystyle 2,00,000 (2 lakh) * Time (n\displaystyle n) = 2\displaystyle 2 years * Annual growth rate (i\displaystyle i) = 5%\displaystyle 5\% p.a. = 0.05\displaystyle 0.05 Substituting the values: PV=2,00,000(1.05)2=2,00,0001.1025≈1,81,405.89≈1.81 lakhPV = \frac{2,00,000}{(1.05)^2} = \frac{2,00,000}{1.1025} \approx 1,81,405.89 \approx 1.81 \text{ lakh} Hence, **Option A** is the correct answer.

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