Say you have a $1,000 repair bill due today and a bond with $1,000 face value. Selling it looks like an easy match.
The issuer still promises $40 of interest plus $1,000 exactly one year from now. But the sale quote is $990.48. Comparable bonds with the same credit risk and one year left offer 5%.
The promised dollars have not changed. What changed is the return buyers can get elsewhere, and that leaves you short of the repair bill.
Start with the promised dollars
The bond's face value is the principal promised back at maturity. It does not set your resale price.
Our bond pays a fixed annual coupon of 4% × $1,000 = $40. It has exactly one payment left: $1,040 in a year. It is noncallable, meaning the contract gives the issuer no right to repay early.
The example keeps the payment date and credit risk fixed, with payment on time and no taxes or trading costs.
If you sell, the buyer pays you and takes over the claim. The issuer receives no new money. Ownership changes; the promised dollars do not.
The buyer changes the price
Paying $1,000 to receive $1,040 in a year earns 4%. A buyer who can earn 5% on a comparable bond needs a lower price for yours.
At 5%, each dollar paid now must become $1.05 in a year. That means price × 1.05 = $1,040. Work backward:
Price = $1,040 ÷ 1.05 = $990.48.
This reverses one year of growth: dividing by 1.05 finds the starting amount. The shortcut works here because there is just one payment, exactly one year away.
Your sale leaves $1,000 − $990.48 = $9.52 of the repair bill unpaid. Waiting a year would bring the full payment, but the bill is due now.
The lower sale price leaves you short while giving the new buyer the return they require.
At a 3% required return, the price is $1,040 ÷ 1.03 = $1,009.71. Buyers can pay more because they need less growth from the same payment.
That is the price-yield relationship: for fixed payments on fixed dates, a higher yield means a lower price, and vice versa. A fixed payment does not mean a fixed price.
A price above face value, also called par, makes this a premium bond; below par, it is a discount bond. These are price labels, not verdicts on whether a bond is a good deal.
Three rates answer different questions
The coupon rate compares annual interest with face value. Current yield compares those same interest dollars with the market price.
Dividing $40 by $990.48 gives a current yield of about 4.04%. The coupon rate is still 4%. The coupon has not grown; the price you divide it by has shrunk.
Yield to maturity (YTM) is the annualized rate that matches the price to all scheduled payments, including principal.
For the new buyer, $40 of interest plus the $9.52 gain from purchase price to face value makes $49.52. Dividing that gain by the $990.48 paid gives a one-year return of 5%. Current yield leaves out the gain toward face value.
The same bond, with a fixed 4% coupon and one year left:
| YTM | Price | Current yield | Versus par |
|---|---|---|---|
| 3% | $1,009.71 | 3.96% | Premium |
| 4% | $1,000.00 | 4.00% | Par |
| 5% | $990.48 | 4.04% | Discount |
At the premium price, the issuer still repays only $1,000 of principal. Subtract the $9.71 premium from the $40 coupon and the buyer gains $30.29 on $1,009.71 invested: 3%. A coupon can stay at 4% while the buyer earns less.
The buyer's 5% or 3% starts with the price they pay you. Your own return depends on what you paid and any coupons you already received.
The formal definition uses present value: YTM discounts every scheduled payment so they add up to the price. With several coupons, each payment date matters; a bond calculator handles that work.
A quoted yield is not a promise
Reinvestment risk means a payment you invest again may earn less. Our bond has nothing to reinvest before maturity.
With several coupons, you can calculate YTM whether you spend them or reinvest them. Matching that rate as compound growth through maturity assumes reinvestment at that yield and payment on time.
A default, an early sale, taxes or trading costs can still change what you earn. A yield calculation cannot make the payments happen.
Try the same idea with $200
Scale the same teaching claim down to $200 of face value and an $8 coupon. What price fits a 5% required return on its $208 payment in one year?
The $200 scales the arithmetic; it does not specify a broker's minimum purchase. If you can explain why its price is below $200, you have the mechanism. Next, Treasuries put it to work across US government payment schedules.
In short
- For fixed promised payments, a higher required yield means a lower price.
- The coupon rate uses face value; current yield uses the market price.
- YTM counts coupons and the gain or loss between purchase price and principal repayment.
- Premium and discount compare price with par. Neither label tells you whether a bond is a good deal.
- Default, early sale, calls, reinvestment and costs can separate your return from a quoted yield.