Question

It is January 9, 2017. The price of a Treasury bond with a 5% coupon that matures on Oct 12, 2030, is quoted as 102-02. What is the cash price? (This bond pays coupons on Oct 12 and Apr 12. Excel might be helpful in calculating the difference in dates.) (required precision: 0.01 +/- 0.01)

Answer 1

There are 89 days between October 12, 2016, and January 9, 2017.

There are 182 days between October 12, 2016, and April 12, 2017.

Accrued Interest = Periodic Coupon Payment * [Days since last payment / Total days in the period]

= [(5%/2)*$100] * [89/182] = $2.50 * 0.4890 = $1.22

Cash Price = Quoted Price + Accrued Interest

= [$102 + (2/32)] + $1.22

= $102.0625 + $1.22 = $103.29