Today is 1 July 2020. Joan has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Joan purchased all instruments on 1 July 2014 to create this portfolio and this portfolio is composed of 27 units of instrument A and 48 units of instrument B. Instrument A is a zero-coupon bond with a face value of 100. This bond matures at par. The maturity date is 1 January 2030. Instrument B is a Treasury bond with a coupon rate of j2 = 4.71% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.

(a) Calculate the current price of instrument A per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ =2.14% p.a.

a. 71.1357

b. 81.6915

c. 71.8968

d. 66.8773

(b) Calculate the current price of instrument B per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ = 2.14% p.a. and Joan has just received the coupon payment.

a. 108.5788

b. 107.4293

c. 106.2238

d. 119.8766

(c) What is the duration of instrument B? Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is j₂ = 2.14% p.a.

a. 2.391

b. 2.840

c. 5.679

d. 4.783

(d) Based on the price in part a and part b, and the duration value in part c, calculate the current duration of Joans portfolio. Express your answer in terms of years and round your answer to two decimal places.

a. 6.07

b. 6.66

c. 4.51

d. 4.54