Time Value of Money

Concept:The cash value is the sum of the down payment and the present value of all future installments, discounted at the given compound interest rate.Explanation:Quarterly interest rate = $12\% / 4 = 3\% = 0.03$.Number of quarterly installments = $4 \times 4 = 16$.Present value of annuity immediate: $PV = P \cdot \frac{1 - (1+r)^{-n}}{r}$.Substitute $P = 3000$, $r = 0.03$, $n = 16$:$(1.03)^{-16} \approx 0.623167$, so $1 - 0.623167 = 0.376833$.$\frac{0.376833}{0.03} \approx 12.5611$, then $PV \approx 3000 \times 12.5611 = 37683.3$.Add down payment $₹5000$ gives total value $\approx 42683.3$.Answer:$₹42683$ (approximately), which matches option C.