A bond with a face value of ₹1,000 matures in 10 years. The nominal rate of interest on bond is 11% p.a. paid annually. What should be the price of the bond so as to yield effective rate of return equal to 8%?

Question

Accepted Answer

> [!TLDR]
> The bond’s price is the present value of all future cash flows (annual interest payments and face value at maturity) discounted at the desired yield of 8%. The calculated price is **₹1,201.30**.

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### Why this approach works

A bond’s price is simply the sum of the present values of all payments it promises. Here, the bond pays ₹110 (11% of ₹1,000) every year for 10 years, and then returns the ₹1,000 face value at maturity. If an investor wants an 8% effective return, they will discount each of these cash flows at 8%. The price today is the amount that, when invested at 8%, would exactly replicate those future receipts.

The key insight: the bond’s coupon rate (11%) is higher than the desired yield (8%), so the bond must trade at a **premium** — above its face value. The price will be more than ₹1,000.

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### Step-by-step calculation

**1. Identify the cash flows**

- Annual coupon payment:  
  $C = 11\% 	imes 1,000 = ₹110$  
- Face value at maturity: $F = ₹1,000$  
- Number of periods: $n = 10$ years  
- Desired yield (discount rate): $r = 8\% = 0.08$

**2. Present value of the coupon annuity**

The coupons form an ordinary annuity of ₹110 per year for 10 years. The present value of an annuity formula is:

$$PV_{	ext{coupons}} = C 	imes \frac{1 - (1+r)^{-n}}{r}$$

Substitute:

$$PV_{	ext{coupons}} = 110 	imes \frac{1 - (1.08)^{-10}}{0.08}$$

First compute $(1.08)^{-10}$:

$$(1.08)^{-10} = \frac{1}{1.08^{10}} \approx \frac{1}{2.158925} \approx 0.463193$$

Then:

$$\frac{1 - 0.463193}{0.08} = \frac{0.536807}{0.08} = 6.7100875$$

So:

$$PV_{	ext{coupons}} = 110 	imes 6.7100875 = ₹738.11$$ …

Q.A bond with a face value of ₹1,000 matures in 10 years. The nominal rate of interest on bond is 11% p.a. paid annually. What should be the price of the bond so as to yield effective rate of return equal to 8%?

Concept understanding — Bond Valuation

Bond Valuation: The Intuition First

The Precise Statement

Why This Works: The Logic

A Worked Example

Why this approach works

Step-by-step calculation

Step 1 — set up the valuation

Step 2 — compute the discount factors (14%)

Step 3 — combine and solve

Step 1 — Identify the cash flows

Step 2 — Discount each cash flow

Step 3 — Add them up

Q.A bond with a face value of ₹1,000 matures in 10 years. The nominal rate of interest on bond is 11% p.a. paid annually. What should be the price of the bond so as to yield effective rate of return equal to 8%?

Why this approach works

Step-by-step calculation

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