Q.What should be the price of the bond to yield an effective interest rate of 8% if it has a face value of ₹1,000 and maturity period of 15 years? The nominal interest rate is 10%.

Bond Valuation: The Intuition First

Imagine you lend ₹1,000 to a friend. You both agree that every year, your friend will pay you ₹80 as interest (8% of ₹1,000). After 5 years, your friend returns your ₹1,000. That's a bond in its simplest form.

A bond is just a loan that can be traded. The person who buys the bond is lending money. The bond's face value (₹1,000) is the amount you get back at the end. The coupon rate (8%) determines the annual interest payment. The maturity (5 years) is when you get your principal back.

Now, here's the key question: What is this bond worth today?

If you could earn 10% interest elsewhere, would you pay ₹1,000 for a bond that only pays 8%? No — you'd demand a discount. If you could only earn 6% elsewhere, that same 8% bond becomes more valuable, and you'd pay a premium.

Bond valuation is simply the process of calculating the fair price of a bond today, given the current interest rates in the market.

The Precise Statement

Where:

• $C$ = annual coupon payment (face value × coupon rate)
• $F$ = face value (principal repaid at maturity)
• $r$ = market interest rate (yield to maturity)
• $n$ = number of years to maturity

This formula says: The bond's price equals the present value of all future cash flows — both the periodic coupon payments and the final face value repayment.

Why This Works: The Logic

You're essentially asking: "If I want to earn a return of $r$ per year, what should I pay today for a stream of future payments?"

Each future payment is discounted back to today using the market rate $r$. The sum of these discounted values gives the fair price.

A Worked Example

Consider a 3-year bond with face value ₹1,000, coupon rate 10%, and market interest rate 8%.

Step 1: Identify the cash flows

• Annual coupon: $C = 0.10 \times 1000 = ₹100$
• Year 1: ₹100
• Year 2: ₹100
• Year 3: ₹100 + ₹1,000 = ₹1,100

Step 2: Discount each cash flow at 8%

• Year 1: $\frac{100}{(1.08)^1} = ₹92.59$
• Year 2: $\frac{100}{(1.08)^2} = ₹85.73$
• Year 3: $\frac{1100}{(1.08)^3} = ₹873.22$

Step 3: Sum them

The bond sells at a premium (₹1,051.54 > ₹1,000) because its 10% coupon beats the market's 8%.

The Big Picture

Bond valuation is present value in action. Every time you see a bond price, you're seeing the market's collective judgment about how much those future payments are worth today, given current interest rates.

The same logic applies to any fixed-income investment: the price is always the present value of promised future cash flows, discounted at the prevailing market rate.