Q.What is the value of the bond, considering a bond has a coupon rate of 10% charged annually, par value being ₹1,000 and the bond has 5 years to maturity. The yield to maturity is 11%.

The key idea is Bond Valuation: the price of a bond equals the present value of all future coupon payments plus the present value of the par value at maturity, discounted at the yield to maturity (YTM).

Step 1 — Identify the cash flows.

Annual coupon = $10\% \times 1,000 = ₹100$.

Par value at maturity = ₹1,000.

Number of periods = 5 years.

Discount rate (YTM) = $11\% = 0.11$.

Step 2 — Present value of coupons (annuity).

$PV_{\text{coupons}} = 100 \times \frac{1 - (1.11)^{-5}}{0.11}$ …

Why this approach works

A bond is simply a stream of cash flows: you receive a fixed coupon each year (here 10% of ₹1,000 = ₹100) for 5 years, and at the end of year 5 you also get back the par value of ₹1,000. The “value” of the bond today is what those future cash flows are worth right now, given the current market interest rate (the yield to maturity, YTM). If the YTM is higher than the coupon rate, the bond sells at a discount — and that’s exactly what we have here (11% > 10%).

The core idea: discount each cash flow back to the present using the YTM as the discount rate, then add them up.

Step‑by‑step calculation

1. Identify the cash flows

• Annual coupon payment: $C = 10\% \times 1{,}000 = ₹100$
• Par value at maturity: $F = ₹1{,}000$
• Number of periods: $n = 5$ years
• Discount rate (YTM): $r = 11\% = 0.11$

2. Present value of the coupon annuity

The coupons form an ordinary annuity of ₹100 per year for 5 years. The formula for the present value of an annuity is:

Plug in the numbers:

First compute $(1.11)^{-5}$:

$1.11^2 = 1.2321$

$1.11^4 = (1.2321)^2 = 1.51807$

$1.11^5 = 1.51807 \times 1.11 = 1.68506$ (approx.)

So $(1.11)^{-5} = 1 / 1.68506 \approx 0.59345$.

Now the annuity factor:

Thus:

$PV_{\text{coupons}} = 100 \times 3.6959 = ₹369.59$ …