Time Value of Money

Concept:Compute the present value of the computer by adding the cash down payment and the present value of the quarterly annuity.Explanation:Cash down payment = ₹5000.Quarterly installment = ₹3000.Number of installments, $n = 4 \times 4 = 16$.Quarterly interest rate $r = \frac{12\%}{4} = 3\% = 0.03$.Present value of annuity = $R \times \frac{1 - (1+r)^{-n}}{r}$.Compute $(1.03)^{-16} = \frac{1}{1.03^{16}} \approx \frac{1}{1.604706} \approx 0.623167$.Then $1 - 0.623167 = 0.376833$.$\frac{3000}{0.03} = 100000$.Present value of annuity $\approx 100000 \times 0.376833 = 37683.33$.Add cash payment: $5000 + 37683.33 = 42683.33$.Thus the value of the computer is approximately ₹42683.Answer:₹42683