Today is 15 November 2021, Sandy just purchased a Treasury bond with a coupon rate of j₂ = 3.105% p.a. and a face value of $100 that matures at par. The purchase price was $98.36. The maturity date of this bond is 15 May 2023.

a) Use linear interpolation to calculate the yield rate. Give your answer in j₂ form, rounded to 3 decimal places. Hint: 1.55% per half year and 2.35% per half year are the lower bound and the upper bound for the linear interpolation

B. b) Calculate the modified duration of this Treasury bond. Assume the yield rate is j₂ = 3.39% p.a. Give your answer in terms of years, rounded to four decimal places.

C f Sandy needs to pay tax, what is her purchase price (rounded to four decimal places)? Given that Sandy needs to pay 30% on coupon payment and capital gain as tax payment. Assume that all tax payments are paid immediately and the yield rate is j₂ = 3.39% p.a.

d) Which of following statement is incorrect?

a.

We can use the duration of this Treasury bond to measure its price sensitivity.

b.

The purchase price of this Treasury bond will decrease, if this Treasury bond is subject to tax payments

c.

The duration of this Treasury bond will be higher if yield rate is higher.

d.

We can use the PV formula in Excel to calculate the bond price if we are given the yield rate