Spot Rates & Discount Factors

Discounting with the Curve

Each future cash flow uses its own maturity's discount factor.

highlighted = computed this step

Use the matching maturity

The curve has discount factors 24/25, 9/10, and 21/25. Each cash flow uses the factor for its own maturity.

PV=∑tCtdt\text{PV}=\sum_t C_t d_t

Discount the cash-flow stream

The cash flows are $5.00, $5.00, and $105.00. Their present values are $4.80, $4.50, and $88.20, for a curve price of $97.50.

P=$5.00d1+$5.00d2+$105.00d3=$97.50P=\$5.00d_1+\$5.00d_2+\$105.00d_3=\$97.50
Discount with the curveEach cash flow uses its matching discount factor.Curve-discounted bond cash flowsPeriodCash flowDiscount factorPV1$5.0024/25$4.802$5.009/10$4.503$105.0021/25$88.20Price = Σ CF × d$97.50

Not one flat yield

Curve discounting is not the same as forcing every maturity through one flat yield. This is descriptive pricing under the stated curve, not investment advice.

one maturity, one discount factor\text{one maturity, one discount factor}