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 2014 to create this portfolio and this portfolio is composed of 37 units of instrument A and 43 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 = 2.23% 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 = 2.79% p.a.

a.

4.890

b.

2.445

c.

2.918

d.

5.835