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Five-rung bond ladder at Treasury par yields: income, duration, cash-flow calendar and roll-overs

ToolBond Ladder
SourceU.S. Department of the Treasury (2026). Daily Treasury Par Yield Curve Rates. Office of Debt Management, Washington, DC, rates of 12 November 2026 (yields only; the ladder is the tool's own illustrative case).
LevelUndergraduate

Problem

Invest 100,000 in five par bonds maturing in 1, 2, 3, 4 and 5 years with coupons every six months. Find the face amount and interest of each rung, the weighted-average yield, the average maturity, the ladder's Macaulay and modified duration, the cash received in each year, and the yearly interest after each of the first three roll-overs if yields stay the same and if every yield rises one point.

Inputs to Enter

  • Amount 100,000; 5 rungs; first maturity 1 year; spacing 12 months; 2 coupons a year; equal face amounts
  • Yields 4.65, 4.86, 4.90, 4.925, 4.95 % (Treasury par yields of 12 November 2026 at 1, 2, 3 and 5 years; the 4-year figure is midway between the 3- and 5-year yields)
  • Change in yields for the roll-over case: 1 point
Open the Bond Ladder tool (loaded with this example)

Answers

  • Face 100,000 / 5 = 20,000 per rung; yearly interest 930 + 972 + 980 + 985 + 990 = 4,857; weighted-average yield 4.857 %; average maturity 3 years
  • Rung 1: i = 0.02325, Macaulay duration 0.9886 years, modified 0.9662; rungs 0.989, 1.930, 2.826, 3.679, 4.490 years; ladder Macaulay 2.783 years, modified 2.716 years; exact price change for a one-point rise −2.66 %
  • Calendar: interest 4,857, 3,927, 2,955, 1,975, 990 (14,704 in all) and 20,000 of principal each year; total paid 114,704
  • Roll-overs into a new 5-year rung at 4.95 %: yearly interest 4,917, 4,935, 4,945 (average yield 4.945 % after three)
  • After a one-point rise (new rung at 5.95 %): yearly interest 5,117, 5,335, 5,545; average yield 5.545 % with 60 % of the ladder rolled
  • Advanced: all in the 1-year rung: interest 4,650, modified duration 0.97, price change −0.96 %; all in the 5-year rung: 4,950, 4.38, −4.27 %

Notes

The tool's default inputs are this case; press Submit. The yields are a dated government figure, not a quotation; the ladder is illustrative and no published worked example is reproduced. The numbers are the tool's own calculation, checked against an independent numpy cash-flow model and the Bond Price and Yield library (test_bond_ladder.php).