Discount vs premium bond
A discount bond prices below face when the market rate sits above the coupon. A premium bond prices above face when it sits below. The same 5 percent 10-year $1,000.00 bond is $857.88 at 7 percent and $1,171.69 at 3 percent.
| Discount bond | Premium bond | |
|---|---|---|
| Cause | Market wants more than the coupon pays. | Market will accept less than the coupon pays. |
| Teaching sheet | 7 percent yield, price $857.88, discount $142.12, current yield 5.83 percent. | 3 percent yield, price $1,171.69, premium $171.69, current yield 4.27 percent. |
| Par for contrast | At 5 percent the same bond is $1,000.00, gap $0.00, current yield 5.00 percent. | Same par sheet. Premium and discount are the two departures from it. |
| Coupon | Still $25.00 twice a year. | Still $25.00 twice a year. The coupon never moved. |
| At maturity | A gain: the bond repays $1,000.00, more than $857.88. | A loss: the bond repays $1,000.00, less than $1,171.69. |
| When you would pick the word | Price below face. | Price above face. |
On this page
The coupon is the same bond
Each half-year coupon is $25.00 on all three sheets. How bond premium and discount work is the gap against face. How bond pricing works is the present value. How current yield works is the coupon over the price.
The bond price calculator prints the gap next to the price.
Current yield sits between coupon and YTM
On the discount sheet, coupon 5 percent, current yield 5.83 percent, YTM 7 percent. On the premium sheet, coupon 5 percent, current yield 4.27 percent, YTM 3 percent. The pull to face is the piece current yield does not count. This is educational material, not financial advice.
Worked examples
Par, for the origin
Face $1,000.00, 5 percent coupon, 5 percent yield, 10 years, two payments a year. Gap?
- Price $1,000.00. Coupon $25.00 twice a year.
- Gap $0.00. Current yield 5.00 percent.
The bond is at par, $1,000.00. Premium or discount is $0.00. Current yield is 5.00 percent. Each coupon is $25.00.
The discount
Same bond, 7 percent yield. What is the discount?
- Price $857.88. Coupon still $25.00.
- Discount $142.12. Current yield 5.83 percent.
The price is $857.88, a discount of $142.12. Current yield is 5.83 percent. Each coupon is $25.00.
The premium
Same bond, 3 percent yield. What is the premium?
- Price $1,171.69. Coupon still $25.00.
- Premium $171.69. Current yield 4.27 percent.
The price is $1,171.69, a premium of $171.69. Current yield is 4.27 percent. Each coupon is $25.00.
Common questions
Is a discount cheap?
It means the coupon sits below the market rate. Cheap is a different question.
Is a premium a bonus?
No. It is the price of richer coupons, bid up until the return equals the lower yield.
Did the coupon change?
No. It stays $25.00. 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.