Bonds Explained

From zero to bond expert — interactive guide covering bonds, interest, pricing, and the yield relationship. No finance degree required.

1. What is a Bond?

The simplest IOU in finance, explained like you're five.

Think of it this way: Your friend needs $1,000 to start a lemonade stand. You lend it to them. They write you an IOU promising to pay you $50 every year (interest), and give back your $1,000 after 10 years (principal). That IOU is basically a bond.

In the real world, the "friend" is a company or government, and the IOU is a formal bond certificate traded on markets.

Key Terms — Visual Chips

Face Value (Par) = $1,000
Coupon Rate = 5%
Coupon Payment = $50/yr
Maturity = 10 years
Yield = Market Return

How the Money Flows

🏦
Investor
You / Lender
Lends $1,000 upfront
Receives $50/year × 10yrs
Gets $1,000 back at maturity
🏛️
Issuer
Company / Govt

Concrete Example

You buy a $1,000 bond with a 5% coupon and 10-year maturity:

You pay $1,000 today
Receive $50 every year (Years 1–10)
Receive $1,000 at Year 10
Total received: $1,500 ($500 interest + $1,000 principal)
Why do companies and governments issue bonds? Because they need to borrow large sums of money. Instead of going to one bank, they split the loan into thousands of small pieces (bonds) and sell them to many investors. You, buying a bond, are essentially being a bank.

2. Simple Interest

The most straightforward way to earn interest — always calculated on the original amount.

Imagine a vending machine: Every year it spits out the same amount of coins. Doesn't matter if last year's coins are sitting there or not — it always calculates from the original amount you put in. That's simple interest.
FV = P × (1 + r × t)  |  Interest = P × r × t

P = Principal  |  r = Annual Rate  |  t = Time (years)

Interactive Simple Interest Calculator

Interest Earned
$1,500
Future Value
$11,500
Per Year
$500/yr
Key Insight: Simple interest is flat. Each year you earn exactly the same dollar amount. You earn interest only on your original principal — never on the interest you've already earned. This is how most bond coupon payments work!

3. Compound Interest

When interest earns interest — the most powerful force in finance.

Snowball rolling down a hill: As the snowball rolls, it picks up more snow. The bigger it gets, the more snow it picks up next roll. Your interest earns its own interest, which earns more interest... the growth accelerates over time.

Einstein (supposedly) called compound interest the "eighth wonder of the world." Whether he said it or not — the math is undeniably powerful.
FV = P × (1 + r/n)^(n×t)

n = compounding periods per year  |  t = years  |  r = annual rate

Interactive Compound Interest Calculator

Compounding Frequency:

Compound FV
-
Interest Earned
-
Simple FV
-
Extra Gain
-

Rule of 72 — Quick Doubling Estimate

Shortcut: Years to double your money ≈ 72 ÷ interest rate (%)

At 5% interest: money doubles in ≈ 14.4 years (exact: 14.2 years)

4. Zero Coupon Bonds

No periodic payments — buy cheap now, get face value later.

Think of it like a savings bond: Instead of paying you $50 every year, the issuer sells you the bond at a discounted price today. You pay less than $1,000 now, wait patiently, and receive the full $1,000 at maturity. No coupons. Just one big payoff at the end.

The "interest" you earn is simply the difference between what you paid and what you receive.
Price = Face Value ÷ (1 + yield)^years

Zero Coupon Bond Pricing Calculator

You Pay Today (Price)
$613.91
You Receive at Maturity
$1,000
Interest Earned
$386.09
Discount from Face
38.6%
Zero Coupon vs Regular Coupon Bond — side by side: A regular bond trickles income back to you every year. A zero coupon bond makes you wait — but the compounding works entirely in your favor because you reinvested everything at the same yield automatically.

5. Coupon Bond Pricing

A coupon bond is just a bundle of zero coupon bonds — each coupon is its own mini-payment discounted back to today.

Think of it as a package deal: You're buying 10 separate IOUs — one for each year's coupon payment — plus one big IOU for the face value. Each IOU is worth less the further away it is (money today > money tomorrow). Add them all up and you get the bond price.
Price = C × [1 − (1+y)^(−n)] / y + FV / (1+y)^n

C = annual coupon payment  |  y = yield  |  n = years  |  FV = face value

Coupon Bond Price Calculator

PV of Coupons
-
PV of Face Value
-
Bond Price
-
Price % of Par
-
YearCash FlowDiscount FactorPresent Value

6. The Yield-Price Relationship

The most important concept in bond investing — and it's beautifully simple once you see it.

Imagine a used car: You bought a car last year that delivers exactly 30 mpg. This year, all new cars deliver 35 mpg. Would anyone pay full price for your 30 mpg car? No — it would have to be cheaper to be attractive. Same with bonds. If new bonds yield more, old bonds must trade at a discount.

PREMIUM

When yield < coupon rate

Price > Par

Bond pays more than market demands → investors bid price up

PAR

When yield = coupon rate

Price = $1,000

Bond pays exactly what market demands → fair price

DISCOUNT

When yield > coupon rate

Price < Par

Bond pays less than market demands → price drops to compensate

Interactive Yield vs Price Demo

$1,000 face value, 10-year bond — drag the sliders and watch the magic:

PAR — $1,000.00

Duration Effect: Longer Bonds Move More

Intuition: A 30-year bond has many more future cash flows that need to be discounted. When yields change, those distant cash flows shift a LOT more in present value than near-term ones. It's like a long lever arm — small force at the end creates big movement.

Both bonds: $1,000 face value, 5% coupon. Drag yield to see the price difference:

5-Year Bond Price
$1,000
at par
30-Year Bond Price
$1,000
at par

7. Current Yield vs Yield to Maturity

Two ways to measure bond return — one is a rough estimate, one is precise.

Current Yield

CY = Annual Coupon / Price

Quick and dirty. Just divides the annual coupon by today's price. Ignores the gain or loss from price returning to par at maturity.

Yield to Maturity (YTM)

IRR of all cash flows

The true annualized return if you hold the bond to maturity. Includes coupon income AND the capital gain/loss from price converging to par.

Interactive: Current Yield vs YTM

Coupon Rate
5.0%
on face value
Current Yield
5.56%
rough estimate
Yield to Maturity
6.27%
precise return

The Three Scenarios

Bond PriceCoupon Rate vs CYCY vs YTMWhy
At Par ($1,000) Coupon Rate = CY CY ≈ YTM No capital gain or loss — all three converge
Discount (<$1,000) Coupon Rate < CY CY < YTM Price rises to par at maturity → extra gain → YTM higher
Premium (>$1,000) Coupon Rate > CY CY > YTM Price falls to par at maturity → capital loss → YTM lower

8. Key Takeaways

Everything you need to remember, in one place.

1

A bond is a loan you give to a company or government. They pay you periodic coupons and return your face value at maturity.

2

Simple interest earns the same fixed amount every period — calculated only on the original principal. Bond coupons work like simple interest.

3

Compound interest earns interest on interest. More frequent compounding = slightly higher returns. Rule of 72: years to double ≈ 72 / rate%.

4

Zero coupon bonds pay no coupons. Bought at a discount, redeemed at face value. Price = FV / (1+y)^n.

5

Coupon bond price = PV of all coupons + PV of face value. Each payment gets discounted back to today using the yield.

6

Yield and price move in OPPOSITE directions. Yield rises → price falls. Yield falls → price rises. This is the most important bond rule.

7

Longer maturity = more price sensitivity to yield changes (higher duration). A 30-year bond swings much more than a 5-year bond for the same yield move.

8

YTM is the true return if held to maturity. It's more accurate than current yield because it includes capital gains/losses to par.

Quick Reference: Premium vs Par vs Discount

Condition Bond Price Yield vs Coupon Rate Investor Gets
PREMIUM > $1,000 (Face Value) Yield < Coupon Rate Coupon rate > market rate → pay up for it
PAR = $1,000 (Face Value) Yield = Coupon Rate Fairly priced — no discount, no premium
DISCOUNT < $1,000 (Face Value) Yield > Coupon Rate Must buy cheap to compensate for low coupon

The Big Picture

Bond = IOU with interest
Price ↑ = Yield ↓
Simple Interest = flat earnings
Compound = exponential growth
Zero coupon = one-time payoff
YTM = true return to maturity
Long maturity = more volatile price
Rule of 72 for quick doubling