How to calculate the price of a semi-annual bond

Semi-annual coupons

Most US government and corporate bonds pay interest every six months. An 8% coupon bond with a $1,000 face value pays $40 twice a year, not $80 once.

Adjust three inputs

To price it, work in half-year periods:

• Coupon per period = annual coupon ÷ 2
• Yield per period = annual yield ÷ 2
• Number of periods = years × 2

Price = (C/2) × [1 − (1 + y/2)^−2T] ÷ (y/2) + F ÷ (1 + y/2)^2T

Example

A 10-year bond, $1,000 face value, 8% coupon paid semi-annually, and a required yield of 6%:

• Coupon per period: $40

• Yield per period: 3%

• Periods: 20

• Value of the coupons: 40 × [1 − 1.03⁻²⁰] ÷ 0.03 = 40 × 14.8775 = $595.10

• Value of the face value: 1,000 ÷ 1.03²⁰ = $553.68

• Price = $1,148.77

In Excel: =PV(6%/2,10*2,80/2,1000) returns −1,148.77.

Compared with annual coupons

The same bond with annual coupons is worth $1,147.20 (see how to calculate a bond price). The semi-annual bond is worth slightly more, because you receive half of each year’s interest six months earlier.

Next: how to calculate yield to maturity.