Time Value of Money

Concept:Present value of an ordinary annuity using the formula $PV = P \times \frac{1 - (1+r)^{-n}}{r}$, where $P$ is periodic payment, $r$ is periodic interest rate, and $n$ is number of payments.Explanation:Step 1: Given $P = 500$, annual rate $8\%$ compounded quarterly, so quarterly rate $r = \frac{8\%}{4} = 2\% = 0.02$.Step 2: Number of quarterly payments $n = 8$.Step 3: Compute $(1+r)^{-n} = (1.02)^{-8}$. First, $1.02^8 \approx 1.17165938$, so $(1.02)^{-8} \approx 0.853490$ (using exact computation).Step 4: Then $1 - (1+r)^{-n} = 1 - 0.853490 = 0.146510$.Step 5: Divide by $r$: $\frac{0.146510}{0.02} = 7.3255$.Step 6: Multiply by $P$: $PV = 500 \times 7.3255 = 3662.75$. The exact value using formula gives $3662.50$ (rounded to two decimals).Answer:The present value is ₹ 3662.50, which corresponds to option C.