How bond premium and discount work
A bond prices below face when the market rate sits above the coupon, and above face when it sits below. A $1,000.00 bond with a 5 percent coupon for 10 years is at par at 5 percent, $857.88 at 7 percent, and $1,171.69 at 3 percent.
Price today
$1,000.00
$25.00 per coupon, twice a year, then $1,000.00 back at maturity. It trades at par.
- Coupon per payment
- $25.00
- Coupon rate, on face value
- 5.00%
- Current yield, on price
- 5.00%
- Premium or discount
- $0.00
What the issuer repays at maturity. Coupons are quoted on this, never on the price.
The annual rate, fixed when the bond is issued, so this one does not move. It is split across the coupons in a year.
What buyers want today on the same risk and maturity. This is the yield to maturity, quoted as an annual rate and split the same way.
Priced on a coupon date, so this leaves a whole number of coupons still to come.
On this page
Next on Models and deals
Current yieldIn short
- At a 5 percent yield the 5 percent coupon bond prices at par: $1,000.00. Premium or discount is $0.00. Current yield is 5.00 percent.
- At 7 percent the same coupons price at $857.88, a discount of $142.12. Current yield rises to 5.83 percent.
- At 3 percent the price is $1,171.69, a premium of $171.69. Current yield falls to 4.27 percent.
- Each half-year coupon is $25.00 either way. The coupon rate never moved. The market rate did, so the price did.
- How bond pricing works is the present value. This page owns the gap against face.
The gap against face value
Premium or discount is price minus face:
A positive gap is a premium. A negative gap is a discount. At par the gap is $0.00.
A $1,000.00 bond paying a 5 percent coupon twice a year for 10 years prices at $1,000.00 when the market wants 5 percent. Each coupon is $25.00. Current yield is 5.00 percent, matching the coupon rate, which is the par case.
The bond price calculator on this page prints that gap next to the price. How bond pricing works is the present value. How current yield works is the coupon over the price. This page is why the price left par.
Market above coupon is a discount
Nothing about the bond changes. Buyers of comparable bonds now want 7 percent. The coupons are still $25.00 twice a year. The price falls to $857.88. The discount is $142.12: the bond changes hands for that much less than the $1,000.00 it repays at maturity.
Current yield rises to 5.83 percent, because the same coupons cost less to buy. Yield to maturity is the 7 percent in the box, above current yield, because the pull to face is a gain the current yield does not count.
Current yield against coupon rate is that split. Discount against premium is the two gaps on one table.
The coupon never moved
Face times the coupon rate, split across two payments, is $25.00 either way. The coupon rate is written into the bond. Between par, discount and premium the only input that moved is the market rate. Mixing a coupon change into a rate move is how a 7 percent yield gets read as a 7 percent coupon.
The gap walks back to zero
As falls, a premium amortises down to face and a discount accretes up to face, if the yield stays put. That walk is not default risk and not a coupon change. How yield to maturity works is the rate that prices the remaining walk. Bond duration is how far the price moves when that yield moves.
What this page is not doing
It is not accrued interest, not a dirty price, and not a default screen. The three sheets are par at $1,000.00 (gap $0.00), a discount of $142.12 at $857.88, and a premium of $171.69 at $1,171.69, all on the same 5 percent 10-year bond with $25.00 coupons. This is educational material, not financial advice.
Worked examples
At par, gap zero
A $1,000.00 bond pays a 5 percent coupon twice a year and matures in 10 years. The market yield is 5 percent. What is the premium or discount?
- Each coupon is $25.00. At a 5 percent yield the bond prices at $1,000.00.
- Premium or discount: $0.00.
- Current yield: 5.00 percent.
The bond is worth $1,000.00 at par. The premium or discount is $0.00. Current yield is 5.00 percent. Each coupon is $25.00.
A \$142.12 discount at 7 percent
Same bond, market yield 7 percent. What is the discount?
- The coupon is still $25.00 twice a year.
- Price falls to $857.88.
- The gap against face is $142.12 the other way: a discount.
- Current yield: 5.83 percent.
The price is $857.88, a discount of $142.12 from the $1,000.00 face. Current yield is 5.83 percent. Each coupon is still $25.00.
A \$171.69 premium at 3 percent
Same bond, market yield 3 percent. What is the premium?
- The coupon is still $25.00 twice a year.
- Price rises to $1,171.69.
- The premium is $171.69.
- Current yield: 4.27 percent.
The price is $1,171.69, a premium of $171.69 over face. Current yield is 4.27 percent. Each coupon is still $25.00.
Common questions
Is a premium a bonus?
No. It is the price of coupons that beat the going rate, bid up until the return on the larger sum equals the market yield. At maturity the bond still repays face.
Why is current yield not the coupon rate off par?
Because current yield divides by price, not face. On the discount sheet that is 5.83 percent against a 5 percent coupon.
Does the gap mean the bond is cheap?
It means the coupon and the market rate disagree. Cheap is a different question. This is educational material, not financial advice.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.