Why does a fixed-rate bond’s price fall when its required yield rises?

Keep the promised payment fixed

Begin with the payment schedule rather than a percentage displayed on a quote. Separate face value, coupon amount, remaining payment dates and the price paid today. Specify whether payments are annual, semiannual or another frequency. A yield number without that convention is difficult to reconcile with a price.

TreasuryDirect explains the relationship between bond prices and yields for U.S. Treasury securities. The exercise here uses a deliberately simpler annual-payment contract. It is not a Treasury auction quote, a current interest rate or an assertion about a particular security’s market value.

Discount one invented payment twice

Suppose an invented bond will pay exactly $1,050 in one year: $1,000 principal plus a $50 final coupon. Stipulate no default, early repayment, fees, taxes, accrued interest or other payments. At a hypothetical annual discount rate of 4%, the present value is $1,050 ÷ 1.04, approximately $1,009.62.

Change only the discount rate to 6%. The same $1,050 payment has present value $1,050 ÷ 1.06, approximately $990.57. The unrounded values differ by approximately $19.05. No coupon changed and no payment disappeared; the amount paid today changed so that the same later payment implies a different yield.

Read the direction without inventing a forecast

At the first price, the bond costs more than its $1,000 face value. At the second, it costs less. The final $50 coupon is the same in both cases, while the gain or loss between purchase price and principal repayment differs. Looking only at the coupon would miss that difference.

These are two alternative valuations at the same hypothetical starting time, not a realized holding-period return. A real bond’s observed price may change for credit, liquidity, supply and demand or other reasons alongside interest rates. The worksheet does not identify which factor caused an actual price movement.

Use a quote-reconciliation checklist

For an actual educational source review, record the settlement date, full remaining cash-flow schedule, payment frequency, quoted-price basis and yield convention. Check whether accrued interest or a transaction charge sits outside the displayed price. Preserve the time at which the quote was observed rather than combining a price from one moment with a yield from another.

For several payments, discount each scheduled payment under a consistent convention and add the results. Do not replace this with coupon divided by price; that is a different yield measure. A callable, floating-rate or inflation-linked contract needs its own cash-flow assumptions rather than the fixed-payment shortcut used here.

Method, sources, and limits

The one-year contract and rates are original hypothetical inputs. Arithmetic and the primary Treasury explanation were checked on 26 October 2026. No bond was selected, priced from live data or purchased. The calculation illustrates an inverse relationship under fixed assumptions; it does not establish credit safety, a future rate path or an investment recommendation.