Calculate a bond's price from its face value, coupon rate, maturity, and the market yield, and see whether it trades at a premium or discount.
How to Use the Bond Calculator
Enter the face value, coupon rate, years to maturity, and the market yield an equivalent bond is currently offering, then pick Annual or Semiannual with the toggle — most real bonds pay semiannually, which is why it's the default.
A bond's price and its yield move in opposite directions, and the mechanism is simple once you see it: the coupon rate is fixed the day the bond is issued, but the market yield an investor could get elsewhere keeps moving. When the market yield rises above the coupon rate, nobody will pay full face value for a bond that pays less than what's available elsewhere — so its price has to drop until the fixed coupon, relative to that lower price, works out to a competitive return. The reverse happens when yields fall below the coupon.
Price = Coupon × [1 − (1 + y)⁻ⁿ] ÷ y + Face Value ÷ (1 + y)ⁿy here is the market yield per period and n the number of periods to maturity — both scaled by the payment frequency, since a semiannual bond has twice as many periods as an annual one over the same term.
Run the defaults — a $1,000 bond, 5% coupon, 10 years, semiannual, against a 6% market yield — and the price comes out to $925.61, a $74.39 discount to face value. That's the market pricing in the fact that a 5% coupon on this bond is worth less than what a fresh 6%-yielding bond of the same risk would pay; buying it below face value is what brings the two into line. Drop the market yield below 5% instead and the same bond would price above $1,000, trading at a premium for the opposite reason.
Total Coupon Payments is just the coupon multiplied by how many payments arrive before maturity — the raw income stream, separate from whatever the bond's price does in the meantime.