Q.A ₹2,000, 8% bond is redeemable at the end of 10 years at ₹105. Find the purchase price to yield 10% effective rate.

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 …