Time Value of Money

Concept:The present value is the amount needed now to grow to a future sum at a given compounded interest rate.Explanation:Step 1: Identify given values.Future value $FV = ₹\,8{,}000$, annual rate $= 6\%$, compounded semi-annually, time $= 6$ years.Step 2: Determine periodic rate and number of periods.Semi-annual rate $r = \frac{6\%}{2} = 3\% = 0.03$.Number of periods $n = 6 \times 2 = 12$.Step 3: Use present value formula for compound interest.$PV = \frac{FV}{(1+r)^n} = \frac{8000}{(1.03)^{12}}$.Step 4: Calculate $(1.03)^{12}$.$(1.03)^{12} \approx 1.425760$.Step 5: Compute present value.$PV = \frac{8000}{1.425760} \approx 5{,}611.03$.Answer:The present value is $₹\,5{,}611.03$, which corresponds to option C.