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 2011 to create this portfolio and this portfolio is composed of 36 units of instrument A and 42 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 = 3.35% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.

(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 = 2.00% p.a.