Your bank purchased a $10,000 T-bond with a settlement date of January 1, 2022 that matures on December 31, 2051, thus the T-bond has exactly 30-years to maturity on the settlement date; where, the next coupon payment will be on June 1, 2022. The coupon rate on the T-note is 1.80% and the market determined YTM is 1.77%.

1. Since the bond pays interest semi-annually, what is the bond's price (both clean and dirty) on 1/1/22, the settlement date? Use both the formula and the Excel Price function:

=Price(settlement,maturity,rate,yld,redemption,frequence,basis) to show that your formula determined price and the Excel determined price are the same. (This part is done for you.)

V_b = (0.0180/2) {[1-((1 + 0.0177/2)^-2(30))]/0.0177/2} + 100%(1 + 0.0177/2)^-2(30)

V_b = (0.0090) {[1-((1 + 0.00885)^-60)]/0.00885} + 1(1 + 0.00885)^-60 ₌

V_b = 0.417568 + 0.589392 = 1.006959 or = 100.6959%

Clean and Dirty PRICE ON 1/1/2022 using Excel
PRICE(settlement,maturity,rate,yld, redemption,frequence,basis)	100.6959461
Settlement date	1/1/2022
Maturity date	1/1/2052
Annual Coupon rate	1.80%
Annual Yield	1.77%
Redemption amount per $100 face value	100
Number of coupon payments per year	2
Day Count basis	0

Thus, using either the formula or Excel, the Clean and Dirty T-bond price is 100.6959% of par value.

1. Three months later, (April 1, 2022), what is the dirty and clean price of the T-bond if the market yield (YTM), because of the FED's "Tapering", increases to 2.10%? Remember, you have held the bond for 89 days or 0.243836 years and the T-note has 29.756164 years or 59.512329 semi-annual periods remaining to maturity. (assume there are184 days during each semi-annual period). Calculate the Clean Price for the T-Bond using both the formula and Excel, as above:

Clean Price

V_b =

Clean PRICE ON 4/1/2022
PRICE(settlement,maturity,rate,yld, redemption,frequence,basis)
Settlement date	4/1/2022
Maturity date	1/1/2052
Annual Coupon rate	1.80%
Annual Yield	2.10%
Redemption amount per $100 face value	100
Number of coupon payments per year	2
Day Count basis	0

1. To calculate the Dirty Price, please calculate the accrued interest on the T-Note given that you have held it for 89 days? (Assume there are184 days during each semi-annual period).

Accrued interest over the 89 days is calculated as:

1. Given that Clean price + Accrued interest =Dirty price,

what is the Dirty price in both percent and in dollar price of the T-bond on April 1, 2022?

Dirty Price = Clean Price + Accrued Interest =

Or Dollar price = $____________