Why is a future payment worth less today?
Consider comparing money at different times. If an alternative investment earns a rate, a smaller amount today can become a larger amount later. The current valuation of a specified future payment is then found by dividing by the accumulation factor. For one period, it is the future payment divided by one plus the rate. This is an educational model showing the direction of dependence, not a search for the “correct” market rate. When the divisor increases while the numerator is unchanged, the result decreases. Interest-rate risk follows from this time-value arithmetic.
Educational hypothetical example: one payment of 2,100 roubles is due after one educational year. At a required yield of 5%, its current value is 2,100 / 1.05 = 2,000 roubles. If required yield becomes 10%, the value is 2,100 / 1.10, approximately 1,909.09 roubles. The difference is approximately −4.55% of the initial value. Neither the payment nor the issuer changed in the model. This is not a real bond, a rate forecast or an expected-profit estimate: only one parameter is changed deliberately to explain the mechanism.
Maturity affects sensitivity
The farther away an unchanged payment is, the more periods participate in discounting. Educational hypothetical example: a single payment of 2,000 roubles in three educational years is valued at 5% as 2,000 / 1.05³, approximately 1,727.68 roubles. At 10% it is approximately 1,502.63 roubles. The decline is approximately 13.03%. In this model the distant payment was more sensitive to the same rate change. The SEC describes the general relationship: longer maturities usually increase interest-rate risk for comparable bonds.[7](#source-market-rate-risk)
With a coupon bond, some money is returned before final maturity. Therefore the final payment date does not exhaust its sensitivity. With other conditions equal, a smaller coupon usually means greater interest-rate risk than a larger coupon.[7](#source-market-rate-risk) This does not establish a universal ranking of all issues: floating coupons, amortization and call rights change the cash-flow structure. Two bonds with the same maturity date can react differently to rates. For comparison, examine when money arrives and which payments are actually known, not only the number of years in the title.
What duration can and cannot do
In a simple model, duration links payment timing to weights in the current price; modified duration is a local estimate of price sensitivity to a small yield change. The key word is local. It cannot be read as a guarantee of an exact fall after any rate jump. For large changes, price nonlinearity matters; for a complex instrument, the expected cash flows themselves may change. Here the concept follows from the discounting model, not from a particular exchange interface method. If a figure is given without the type of duration and assumptions, comparison may be wrong.
Counterexample to “all bonds fall alike”: with a floating coupon, a future payment may reset along with a reference rate.[9](#source-market-corporate-bonds) That changes the calculation but does not make the bond risk-free: the reset can lag, be capped or use a different reference. Another counterexample is an improvement in perceived credit risk at the same time as rates rise. A lower additional risk premium may partly offset the rate effect. Thus price observation alone cannot separate interest-rate risk from credit risk; the bond terms and a careful causal model are needed.
Holding to maturity does not cancel other questions
If an ordinary bond performs under its contract, an interim price change does not change its fixed schedule. But holding to the end does not guarantee the debtor’s ability to pay or protect the purchasing power of the money.[8](#source-market-bond-risks) Moreover, the owner’s plans may change: if an early sale becomes necessary, calculated price sensitivity becomes a direct cash question. Guarantees of particular payments must not automatically be extended to the market sale price.[7](#source-market-rate-risk) This analysis separates situations; it does not recommend an investment horizon, predict future rates or determine a personally acceptable loss.