Today is 1 July 2020. Sandra has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Sandra purchased all instruments on 1 July 2011 to create this portfolio and this portfolio is composed of 22 units of instrument A and 22 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 = 3.46% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023

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 = 2.99% p.a.

a.

4.834

b.

5.753

c.

2.417

d.

2.876