Final answer:
To find Luciana's purchase price for the Treasury bond, we can calculate the present value of the bond's future cash flows using the bond's coupon rate, face value, yield, and time to maturity. The purchase price is $101.1594, rounded to four decimal places.
Step-by-step explanation:
To find Luciana's purchase price, we need to calculate the present value of the bond's future cash flows. The bond has a face value of $100 and a coupon rate of 3.88%, which means it pays $3.88 in interest each year. The bond matures on 15 April 2029. Luciana purchased the bond on 18 February 2018, which means there are 11 years until maturity. The yield is 3.9% p.a. compounded half-yearly.
Using the formula for the present value of a bond, we can calculate the purchase price as follows:
PV = (C * (1 - (1 + r/n)^(-n*t)) / (r/n)) + (F * (1 + r/n)^(-n*t))
Where PV is the purchase price, C is the coupon payment, r is the yield rate, n is the number of compounding periods per year, F is the face value, and t is the time to maturity in years.
Plug in the values:
C = $3.88, r = 3.9%, n = 2 (compounded half-yearly), F = $100, t = 11 years
Calculating this gives us a purchase price of $101.1594, rounded to four decimal places.