Today is 1 July, 2019. Carole has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Carole purchased all instruments on 1 July 2012 to create this portfolio, which is composed of 39 units of instrument A and 30 units of instrument B.

• Instrument A is a zero-coupon bond with a face value of $100. This bond matures at par. Its maturity date is 1 January 2029.
• Instrument B is a Treasury bond with a coupon rate of j₂=3.75% p.a. and a face value of $100. This bond matures at par. Its maturity date is 1 January 2022.

What is the duration of instrument B? Express your answer in terms of years and round your answer to three decimal places. Assume a yield rate of j₂=4.99% p.a.

a.

2.862 years

b.

2.408 years

c.

4.816 years

d.

5.725 years