Question

You buy a Treasury bond on Feb 4, 2019. The bond last paid a coupon on Dec 31, 2018, and always pays a coupin on the last day of the month when it is due. The bond matures on Dec 31, 2028, has par value of $1,000, 2% coupon paid semi-annually, and 3% YTM. Assume that the bond's day-count convention is the standard for Treasuries.

What is the full price of this bond?

Round your answer to 2 decimal places.

Answer 1

Coupon = 2% *1000 = 20

Semi annual Coupon = 20 / 2 = 10

YTM = 3%

Semi annual YTM = 3% / 2 = 1.5

Number of period = 10 * 2 = 20

Face Value = 1000

Bond price = ?

Bond clean price = Coupon * (1-((1+YTM)^(-Number of periods))/YTM)+(Face value/((1+YTM)^Number of periods)

Bond clean price = 10*((1-((1+1.5%)^(-20)))/1.5%)+(1000/((1+1.5%)^20))

Bond clean price = 914.16

Accrued Interest = F * (r/(PY)) * (E/TP)

Where:

F = Face value of the bond

r = Coupon rate

PY = Payments a Year

E = Days elapsed since last payment

TP = Time between payments (from above description).

Accrued Interest = 1000 * (2%/(2)) * (35/360)

Accrued Interest = 0.97

Accrued Interest = 0.97 * 2

Accrued Interest = 1.94

Bond dirty price = Clean price + Accrued Interest

Bond dirty price = 914.16 + 1.94

Bond dirty price = 916.10