Enter the face value, coupon rate, years to maturity, payment frequency, and the market's required yield to find the bond's fair price and current yield.
Set the market rate to match this page's own 5% coupon rate exactly, holding everything else the same, and the price lands on exactly $1,000.00 — the face value, to the cent. That is not a coincidence: when a bond's fixed coupon already matches what the market currently demands, there is no reason for its price to sit above or below face value at all. Every deviation from par traces back to a gap between those two rates, in one direction or the other.
This page's own default bond has a current yield of 5.40% — but its yield to maturity is exactly 6%, since that 6% market rate is what its $925.61 price was discounted at in the first place. Current yield only counts coupon income against today's price; it says nothing about the $74.39 capital gain still to come as the price rises to $1,000 at maturity. For a bond bought at a discount, current yield always understates the total return an investor actually earns by holding to maturity.
This page's price is two present-value calculations added together: 20 semi-annual coupon payments treated as an annuity, plus the $1,000 face value treated as a single lump sum, both discounted at the same 3%-per-period market rate. The Annuity Calculator models a growing payment stream on the way in; a bond's coupons are that same idea running in reverse, valuing a fixed payment stream on the way out instead. The Present Value Calculator reproduces either half by hand, and the Investment Calculator covers lump-sum growth without a bond's periodic coupon structure at all.
A bond's coupon payments are fixed at issuance, so when market interest rates rise, newly issued bonds offer better yields, making the older, lower-fixed-coupon bond less attractive by comparison — its price has to fall so its effective yield rises to match the new market rate. The reverse happens when market rates fall: the old bond's fixed coupon suddenly looks relatively better, so its price rises above face value.
Coupon rate is the fixed annual rate stated on the bond at issuance, based on face value — it never changes. Current yield is annual coupon income divided by the bond's current market price, so it moves as the price moves. Yield to maturity (YTM) is the total return if held to maturity, factoring in price, all coupon income, and any gain or loss from buying at a premium or discount — it's the most complete measure of the three, though this calculator focuses on price and current yield.
A bond trades at a premium when its price is above face value, which happens when its coupon rate is higher than the current market yield — investors are willing to pay extra for the above-market coupon. It trades at a discount when its price is below face value, because its coupon rate is lower than the market yield and the price has to fall to make up the difference. A bond priced exactly at face value is trading at par.
Most bonds pay interest semi-annually — twice a year — which is why this calculator defaults to 2 payments per year, but annual, quarterly, and even monthly payment schedules exist depending on the issuer and market. For general lump-sum growth without a bond's periodic coupon structure, see the Investment Calculator.
Worked example: a $1,000 face-value bond with a 5% annual coupon rate, 10 years to maturity, semi-annual payments, and a 6% required market yield. The semi-annual coupon payment is 1,000 × 5% ÷ 2 = $25, discounted at 3% per period across 20 periods, plus the $1,000 face value discounted back the same 20 periods. That works out to a price of $925.61 — a discount to face value, since the 5% coupon is below the 6% market yield. Total coupon income over the bond's life is 25 × 20 = $500, and the current yield is 50 ÷ 925.61 ≈ 5.40%.
What a bond price actually is. A bond’s fair price is the present value of its coupon stream plus the present value of the face amount returned at maturity, both discounted at the yield the market currently demands. That is why prices fall when yields rise: the same future cash flows are being discounted harder. You can reproduce either half of it by hand with the present value calculator — the coupons as an annuity, the redemption as a lump sum.