Tools › Investing › Bonds › Bond Price and Yield › Example

8¾ % 30-year Treasury bond priced at a yield of 8.84 % (31 CFR Part 356, Appendix B, example A)

ToolBond Price and Yield
SourceU.S. Department of the Treasury (2014). Sale and Issue of Marketable Book-Entry Treasury Bills, Notes, and Bonds: Formulas and Tables. 31 CFR Part 356, Appendix B, Bureau of the Fiscal Service, Washington, DC. Section II, example A (price) and example D (accrued interest).
LevelUndergraduate

Problem

An 8¾ % 30-year bond issued May 15, 1990 and due May 15, 2020 pays interest every six months. Find its price per 100 of face value at a yield to maturity of 8.84 %, then its current yield, duration and convexity, and the price change for a one-point move in yield.

Inputs to Enter

  • Face value 100, coupon rate 8.75 %, 2 coupons per year, 30 years to maturity
  • Solve for price from yield; yield to maturity 8.84 %
Open the Bond Price and Yield tool (loaded with this example)

Answers

  • Coupon 4.375 each half-year; yield per period 0.0442; 60 coupons
  • Price = 4.375 × 20.935719 + 100 × 0.074641 = 99.057893 per 100 (regulation 99.057893)
  • Current yield 8.833 %; yield from the price 99.057893 solves back to 8.8400 % in four Newton iterations
  • Macaulay duration 10.945 years, modified duration 10.482, convexity 188.81
  • Yield up one point: −10.38 by duration, −9.45 with convexity, −9.51 exact; down one point: +10.38, +11.32, +11.39
  • Advanced, example D (9½ % note at 9.54 %, settled 1985-11-29, due 1995-11-15): 14 of 181 days elapsed, accrued interest 0.367403 (regulation .367403)

Notes

The tool's default inputs are example A; press Submit. Between coupon dates the tool discounts the fractional period at compound interest (market convention) and the regulation at simple interest, so example D's clean price is 99.738573 on the page against 99.730918 in the regulation; the accrued interest is the same.