The Time Traveler’s Bond: A Story of Bond Pricing

In the grand city of Financia, where markets roared and traders bustled, a young economist named Elara discovered an ancient book titled The Art of Bond Valuation. Intrigued, she flipped through the yellowed pages and was suddenly engulfed in a golden light.

When she opened her eyes, she found herself in the Bond Bazaar, a mysterious marketplace where traders weren’t just selling ordinary assets—they were selling promises of future payments.

A wise old trader named Master Theo greeted her.

“Ah, a new visitor! You must learn the art of bond pricing before you can leave.”

Lesson 1: Understanding Bonds

Elara watched as a merchant named Darius sold a 10-year bond to a buyer.

“This bond promises ₹1,000 at the end of 10 years,” Darius said. “And it pays ₹50 in interest every year.”

Elara’s eyes widened. “So, bonds are just loans?”

Theo nodded. “Exactly! And the price of a bond today depends on what people expect to receive in the future.”

Lesson 2: The Present Value of Future Cash Flows

Theo handed Elara a golden scale. “To price a bond, you must weigh its future payments. But there’s a trick—money today is worth more than money in the future.”

He pointed to a glowing formula floating in the air:

$$P = \sum \frac{C}{(1+r)^t} + \frac{F}{(1+r)^T}$$

Where:

• $P$ = Price of the bond
• $C$ = Coupon payment (interest)
• $r$ = Discount rate (market interest rate)
• $t$ = Time period
• $F$ = Face value of the bond (₹1,000 in this case)
• $T$ = Total time until maturity

Theo explained, “Each future payment must be discounted to today’s value. The higher the interest rate, the less future cash flows are worth today.”

Lesson 3: The Role of Interest Rates

Elara noticed that when interest rates rose, bond prices fell, and vice versa.

She saw two traders arguing:

• One held a bond issued when rates were 5%, paying ₹50 annually.
• The other had a new bond issued at 7%, paying ₹70 annually.

The buyer frowned at the old bond. “Why would I buy this when I can get a bond that pays ₹70 instead?”

Darius sighed and lowered the price of his 5% bond until it matched the return of the 7% bond.

Elara gasped. “So when interest rates rise, bond prices fall because older bonds become less attractive!”

Theo smiled. “Exactly. And when rates fall, older bonds with higher interest rates become more valuable.”

The Final Test: Pricing a Bond

Theo challenged Elara to price a bond herself:

• 5-year bond
• ₹100 annual coupon
• ₹1,000 face value
• Market rate: 6%

Using the formula, she calculated:

$$P = \frac{100}{(1.06)^1} + \frac{100}{(1.06)^2} + \frac{100}{(1.06)^3} + \frac{100}{(1.06)^4} + \frac{100}{(1.06)^5} + \frac{1000}{(1.06)^5}$$

After solving, the bond price came out to ₹1,048.

The market erupted in applause!

Theo laughed. “You have learned the secret of bond pricing! Now, you may return.”

A flash of light engulfed Elara, and she found herself back in her room, holding the ancient book. She smiled—she had just cracked the code of the bond market.

[Finance]