MAT-144 · Mathematical Reasoning Topic 07 · Taxes & Stocks
Lesson 05 · Lending the company money

Bonds: face value, coupon, yield.

A bond is a loan you make to a company or government, in exchange for regular interest payments and the return of your principal at maturity. The flip side of a stock: lender, not owner.

01Face value · par 02Coupon rate 03Yield
▸ THE HOOK

When a company wants to raise money, it has two basic options: sell stock (give up partial ownership in exchange for cash, as in Lesson 4) or sell bonds (borrow money in exchange for a promise to pay interest and return the principal at a specified date). Governments do the same: U.S. Treasury bonds, municipal bonds, sovereign debt from other countries — all are the same financial instrument applied at different scales.

A bond is fundamentally simpler than a stock. When you buy a $1,000 face-value bond with a 5% coupon rate and a 10-year maturity, the terms of the contract are fixed in advance: every year for ten years you receive $50 in interest, and at the end of year 10 you get your $1,000 back. The company is contractually obligated to make those payments; if it cannot, it is in default, and you (as a creditor) have legal claims on the company's assets that stockholders do not.

This certainty is the bond's main appeal — and the source of its lower expected return compared to stocks. You give up upside potential in exchange for predictability. This lesson develops the bond vocabulary (face value, coupon, yield) and the arithmetic of a typical bond's life cycle.

Face value, coupon, yield: the three numbers.

Three numbers fully describe a typical fixed-rate bond. The face value (also called par value) is the amount the issuer promises to return at maturity — almost always $1,000 in U.S. corporate bonds, regardless of what you actually paid for the bond. The coupon rate is the annual interest rate paid on the face value; a 5% coupon on a $1,000 bond pays 0.05 × 1,000 = $50 per year. The maturity date (or term, in years) is when the issuer returns the face value and the bond expires.

Bond prices can drift above or below face value in the secondary market, depending on prevailing interest rates. The current yield is the annual coupon payment divided by the current price (not the face value):
current yield = annual coupon / current price

Bonds trading below face value (called discount bonds) have current yields above their coupon rate; bonds trading above face value (premium bonds) have current yields below their coupon rate. The two move inversely with price.
THE LIFE OF A BOND $1,000 face value · 5% coupon · 10-year maturity Year 0 BUY −$1,000 1 +$50 2 +$50 3 4 ··· $50 every year 8 9 +$50 Year 10 MATURITY +$50 final coupon +$1,000 principal total received: 10 × $50 + $1,000 = $1,500 $500 of interest earned over 10 years on $1,000 lent

A $1,000 face-value bond with 5% coupon, 10-year maturity. Buy for $1,000 in year 0; receive $50 each year for ten years (annual coupon payments); receive the $1,000 face value back at maturity in year 10. Total received: $1,500. Total interest earned: $500.

▸ DEFINITION

A bond is a fixed-income security: the issuer promises to pay regular coupon payments (equal to face value × coupon rate per year) and to return the face value at maturity. The current yield of a bond is annual coupon / current market price, and may differ from the coupon rate if the bond trades above or below face value.

Words you'll see on every bond quote

  • Face value (par) The amount the bond's issuer promises to return at maturity. Almost always $1,000 for U.S. corporate bonds; sometimes $5,000 or $10,000 for institutional issues; sometimes smaller for retail-oriented products.
  • Coupon rate The annual interest rate the bond pays, as a percentage of face value. A 5% coupon on a $1,000 bond pays $50 per year. Often paid in two semiannual installments of $25 each, though introductory courses simplify to annual payments.
  • Maturity The date (or remaining number of years) until the bond's face value is returned. U.S. Treasury bonds run up to 30 years; corporate bonds commonly 5, 10, or 20 years. Longer maturities expose the investor to more interest-rate risk.
  • Current yield Annual coupon divided by current market price, expressed as a percent. A $50 coupon on a bond currently trading for $1,025 has a current yield of 50/1,025 ≈ 4.88%. The current yield differs from the coupon rate whenever the bond's market price differs from its face value.
  • Premium vs discount A bond trading above face value is a premium bond (price > $1,000); below face value is a discount bond (price < $1,000). Prices drift based on prevailing interest rates: when rates rise, existing bonds become less attractive and their prices fall (discount); when rates fall, existing bonds become more attractive and their prices rise (premium).

A standard $1,000 corporate bond.

Compute the annual coupon, the total interest earned over the bond's life, the total amount received, and the current yield if the bond is trading at a discount.

"You buy a corporate bond with face value $1,000, coupon rate 5%, and 10-year maturity. The bond currently trades on the secondary market at $950 (a discount). Compute the annual coupon payment, the total interest earned over 10 years if held to maturity, the total amount received, and the current yield."

1

Compute the annual coupon payment.

Annual coupon = face value × coupon rate:

annual coupon = $1,000 × 0.05 = $50

Paid every year for the bond's 10-year life.

→ same every year
2

Total interest earned over 10 years.

total interest = 10 × $50 = $500
→ 10 coupon payments summed
3

Total amount received.

At maturity, the bondholder receives the face value back, in addition to the coupons collected over the life:

total = interest + face value = $500 + $1,000 = $1,500
→ life-of-bond total
4

Current yield at the discount price.

The bond trades at $950, not $1,000. Current yield divides the coupon by the market price:

current yield = $50 / $950 ≈ 0.0526 = 5.26%

The discount price means a new buyer today earns 5.26% effective yield on their $950 investment, slightly higher than the bond's nominal 5% coupon rate. Plus, at maturity they receive $1,000 back — a $50 capital gain on top of the coupons.

→ discount → yield > coupon rate

Three bonds. Compute the key numbers.

Same recipe. Watch the relationship between current yield and coupon rate when the price is above vs below face value.
PROBLEM 01 ☆ ☆   warm-up · annual coupon

A corporate bond has face value $1,000 and coupon rate 4.5%. What is the annual coupon payment in dollars?

annual coupon = $
PROBLEM 02 ★ ★ ☆   total amount received

A bond has face value $1,000, coupon rate 6%, and 8-year maturity. What is the total amount received if held to maturity?

total = $
PROBLEM 03 ★ ★ ★   current yield at a premium

A bond with face value $1,000 and coupon rate 6% is currently trading at $1,050. What is the current yield, rounded to two decimal places?

current yield % =

Three fast questions before you move on.

Tap an answer. Feedback shows up immediately.

Q1. Buying a bond means you are:

Why B? A bond is a loan; the bondholder is a creditor, not an owner. A describes a stockholder. Bondholders have priority over stockholders if the company goes bankrupt, but they do not share in company profits beyond the contractually-specified coupon.

Q2. A bond's annual coupon payment is computed against:

Why B? The coupon payment is locked at issuance: face value × coupon rate. It does not change as the bond's market price moves. The current yield (coupon / price) is what changes with price.

Q3. If a bond trades at a discount (below face value), its current yield is:

Why C? Discount means price < face value. Since the annual coupon is fixed (face × rate), dividing by a smaller denominator (the discounted price) produces a larger yield. The opposite is true for premium bonds (yield < coupon rate).
▸ UP NEXT — LESSON 06

The lender, not the owner.

Bonds are the predictable counterpart to stocks. A bondholder knows almost exactly what they'll receive across the life of the bond: the coupon payments are contractually fixed, the face value is returned at maturity, and the only real risk is the issuer going bankrupt before the bond matures. That credit risk is the principal reason different bonds have different coupon rates: U.S. Treasury bonds (effectively zero credit risk) pay lower coupons than investment-grade corporate bonds, which pay lower coupons than high-yield ("junk") bonds whose issuers carry meaningful default risk.

Bonds are central to retirement planning. As investors approach retirement, they typically shift money out of stocks (which can drop sharply at inopportune times) and into bonds (whose stream of payments matches the steady spending pattern of retirement). This is the subject of the next lesson and the closer of the course.

Next: Lesson 6, the topic and course finale — diversification and the stock-bond split. Why a real-world portfolio combines both, how the mix changes with time horizon, and how everything you've learned in Topics 1-7 comes together in a single financial-literacy worldview.

Continue to Lesson 06

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