Meet Diana. She has $9,400 sitting in cash and a quote in front of her: a corporate bond with a 5% coupon, a $1,000 face value, and 8 years left until it matures. The catch that makes her pause is the price. The bond is not selling for $1,000. It is selling for $940, a $60 discount to par.
Her first instinct is the one almost everyone has: the bond pays 5%, so she will earn 5%. That instinct is wrong, and the gap matters more than the small discount suggests.
Start with the cash. A 5% coupon on a $1,000 face value pays $50 a year, every year, no matter what Diana paid for the bond. The coupon is fixed to the face value, not to her purchase price. But Diana did not spend $1,000. She spent $940. Divide the same $50 by what she actually put in and her current yield climbs to about 5.32%. The discount quietly raised her income return before a single other thing happened.
Then comes the part the coupon rate hides completely. Diana bought the bond for $940, but at maturity the issuer redeems it for the full $1,000 face value. That is a $60 gain baked into the contract, collected on the day the bond comes due. It is not a maybe. It is written into the bond's terms. Spread that gain across the 8 years she holds it and fold it together with the annual coupons, and you get the number that actually measures her return: yield to maturity.
Picture the two pieces stacked. Over 8 years Diana collects $50 a year, or $400 in coupons. On top of that sits the $60 she earns simply by holding the bond from $940 up to $1,000. The coupon rate counts only the first piece. The current yield counts the first piece against the right denominator. Neither one counts the $60. That is why both numbers undersell what Diana is really earning.
For Diana's bond, the yield to maturity works out to roughly 5.9%. That is the headline. She is buying a bond with a 5% coupon, and her true annualized return is closer to 5.9%, because she bought it below par and gets pulled back up to face value at the finish line. The coupon told her 5%. The current yield told her 5.32%. Only the yield to maturity told her the whole story.
This is the entire reason a yield calculator exists. A discount bond's real return lives above its coupon, and a premium bond's real return lives below it. The three yields rarely match, and the one that matters most, yield to maturity, is the one you cannot work out in your head. This tool runs that math for you the moment you enter a price, a coupon, and a maturity.