Today is 15 November 2018. To construct a portfolio, Jake just purchased two different Treasury bonds, henceforth referred to as Bond A and Bond B. Assume the yield rate for these financial instruments was j₂ = 3.15% p.a.

Bond A has a coupon rate of j₂ = 3.05% p.a. and a face value of $100. The maturity date of this bond is 15 May 2020.

Bond B has a coupon rate of j₂ = 2.95% p.a. and a face value of $100. The maturity date of this bond is 15 January 2022.

a. Calculate the duration and the modified duration of Treasury bond A. Give your answer in terms of years, rounded to three decimal places.

b. Calculate the price Jake paid for bond A (rounded to three decimal places).

c. Calculate Jakes purchase price of bond B using the RBA approach (rounded to three decimal places).

d. Jake purchased 101 units of bond A and 199 units of bond B to establish his portfolio. Based on your results from part a, b and c, calculate the duration of Jakes portfolio, given that bond B has duration of 3.016 years. Give your answer in terms of years, rounded to two decimal places.