Solve for a fixed-rate coupon bond's price, face value, yield, time to maturity, or coupon — given the other four, valued on a coupon date.
A bond's coupon payments are fixed the moment it's issued — they never change. When market yields rise above the bond's coupon rate, investors won't pay full face value for a stream of below-market payments, so the price has to drop until the bond's effective return matches the market. When yields fall below the coupon rate, the opposite happens: the bond's fixed payments look attractive, and investors bid the price up above face value. This inverse relationship is one of the most fundamental facts in fixed-income investing.
A bond priced exactly at its face value is trading "at par" — this happens precisely when the yield equals the coupon rate. Trade above face value and it's at a "premium" (yield below coupon); trade below and it's at a "discount" (yield above coupon). All three are just different snapshots of the same price-yield relationship.
More frequent coupon payments mean your money gets reinvested (compounds) more often, which slightly changes both the bond's fair price and its effective yield compared to the same nominal rate paid less frequently.
This is the bond's yield to maturity (YTM) — the total return you'd earn if you bought the bond today and held it until it matures, accounting for both coupon payments and any difference between the purchase price and face value.
Not by itself — what matters is the yield relative to the price paid, not the coupon rate in isolation. A high-coupon bond bought at a steep premium can yield less than a low-coupon bond bought at a discount.
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