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Mathematics

Bond Pricing and Yield

Coupons, Discount Rates, and Why Prices Move Opposite Yields — A TLDR Primer

Bond pricing shows up on finance exams, in AP Economics classes, and in every personal investing conversation — yet most students hit the same wall: why does a bond's price fall when interest rates rise? And what exactly is yield to maturity?

**Bond Pricing and Yield** cuts straight to the answers. This concise primer walks you through the math and the intuition behind fixed-income securities, from the basic structure of a bond to the discounted cash-flow formula that determines its price. You'll learn how yield to maturity works as an internal rate of return, why current yield and coupon rate are different things, and how duration gives you a quick estimate of interest-rate risk — the kind of understanding that separates students who memorize formulas from those who actually get it.

The guide is short by design. No filler, no multi-chapter detours through accounting theory. Each section leads with the single most useful idea, backs it up with worked numbers, and flags the misconceptions students most often carry into exams. The final section connects bond math to mortgages, student loans, and central bank policy — so the concepts land in the real world, not just on a problem set.

If you're preparing for a finance or economics exam, tutoring a student on fixed-income basics, or just tired of explanations that assume you already know the answer, this is the place to start. Pick it up and work through it today.

What you'll learn
  • Identify the cash flows of a standard coupon bond (face value, coupon, maturity).
  • Price a bond by discounting its cash flows at a given yield.
  • Compute and interpret yield to maturity, current yield, and coupon rate.
  • Explain the inverse relationship between bond price and yield.
  • Use duration to estimate how bond prices respond to interest rate changes.
What's inside
  1. 1. What a Bond Actually Is
    Introduces bonds as loan contracts with a fixed cash-flow schedule and defines the core terms.
  2. 2. Pricing a Bond by Discounting Cash Flows
    Builds the present-value formula for a coupon bond and works through numerical pricing examples.
  3. 3. Yield to Maturity and Other Yield Measures
    Defines YTM as the internal rate of return on a bond and contrasts it with current yield and coupon rate.
  4. 4. Why Price and Yield Move in Opposite Directions
    Explains the inverse price-yield relationship intuitively and mathematically, with examples of rate changes.
  5. 5. Duration: Measuring Interest Rate Sensitivity
    Introduces Macaulay and modified duration as tools to estimate how much a bond's price changes when yields move.
  6. 6. Why This Math Shows Up Everywhere
    Connects bond pricing to mortgages, student loans, central bank policy, and personal investing decisions.
Published by Solid State Press
Bond Pricing and Yield cover
TLDR STUDY GUIDES

Bond Pricing and Yield

Coupons, Discount Rates, and Why Prices Move Opposite Yields — A TLDR Primer
Solid State Press

Bond Pricing and Yield

Coupons, Discount Rates, and Why Prices Move Opposite Yields — A TLDR Primer

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Contents

  1. 1 What a Bond Actually Is
  2. 2 Pricing a Bond by Discounting Cash Flows
  3. 3 Yield to Maturity and Other Yield Measures
  4. 4 Why Price and Yield Move in Opposite Directions
  5. 5 Duration: Measuring Interest Rate Sensitivity
  6. 6 Why This Math Shows Up Everywhere
Chapter 1

What a Bond Actually Is

When a company or government needs money, it has two basic choices: sell ownership (equity) or borrow. A bond is a borrowing instrument — a formal, written promise to repay a loan on a specific schedule. The buyer of the bond is the lender; the issuer (the entity that creates and sells the bond) is the borrower.

What makes a bond different from an ordinary bank loan is that the repayment schedule is completely fixed at the start and written into a contract. That predictability is the whole point: investors buy bonds precisely because the cash flows are known in advance.

The three things every bond tells you

Every standard bond specifies three things from the moment it is issued:

  1. Face value — the lump sum the issuer promises to repay at the end. Also called par value, this is typically $1,000 for corporate bonds in the US. It is not necessarily what you pay for the bond today; it is what the issuer owes you at the finish line.

  2. Coupon rate — the annual interest rate, expressed as a percentage of face value, that determines how much the issuer pays you periodically until maturity. If a bond has a face value of $1,000 and a 6% coupon rate, it pays $60 per year in interest. Most bonds pay in two installments every six months, so that would be two payments of $30. The word "coupon" is historical: bonds once had physical tear-off coupons that holders mailed in to collect interest.

  3. Maturity — the date on which the issuer repays the face value and the bond contract ends. A "10-year bond" issued today matures in ten years. Maturities range from a few weeks to a year (Treasury bills) to 30 years or more (long-term corporate or government bonds).

Together, these three pieces of information define the bond's entire cash-flow schedule — every dollar the bondholder will ever receive, and when.

About This Book

If you are a high school student who needs bond pricing and yield explained simply for a personal finance or economics class, a college freshman working through intro to bonds for finance class assignments, or a self-studier who keeps hearing "interest rates move prices" without understanding why, this book is for you. It is also useful for parents helping a student review and for anyone prepping for standardized exams that touch fixed income concepts.

The book covers discounted cash flow bonds study guide material in a tight sequence: what a bond is, how to price it, yield to maturity explained for beginners, and the inverse relationship that makes how bond prices and interest rates relate so counterintuitive at first. It closes with bond duration and interest rate risk, the key tool for measuring price sensitivity. Fixed income math for a high school student or early college reader, concise and with no filler.

Read straight through, work each numbered example, then attempt the problem set at the end to check your understanding before an exam.

Keep reading

You've read the first half of Chapter 1. The complete book covers 6 chapters in roughly fifteen pages — readable in one sitting.

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