A bond's price is the present value of its coupons plus its face value at maturity.
A bond value calculator estimates what a bond is worth today by discounting its future coupon payments and face value back to the present at the current market interest rate. It shows whether a bond trades at a premium or a discount.
A bond's price is the present value of its fixed future payments. When market rates rise, those fixed payments are worth less compared to newly issued bonds paying more, so the price falls below face value, a discount. When rates fall, the bond's above-market coupons become attractive and it trades above face value, a premium. This inverse relationship is the single most important idea in bond investing.
The coupon rate is fixed at issue and sets the dollar payments; the yield is the return based on today's price. If you buy a bond at a discount, your yield is higher than the coupon rate because you also gain as the price rises toward face value at maturity, and vice versa for a premium. Longer-maturity bonds are more sensitive to rate changes, so their prices swing more when rates move.
By discounting its future coupon payments and face value to the present at the current market rate. The sum of those present values is the bond's price.
A bond's coupons are fixed, so when new bonds pay more, the older bond is worth less to match the higher market yield. Its price drops below face value.
The coupon rate is the fixed payment set at issue; the yield reflects the return at today's price. They match only when the bond trades exactly at face value.
See the exact formula and a worked example on our methodology page.