Today is 1 July, 2019. Camilla has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Camilla purchased all instruments on 1 July 2015 to create this portfolio, which is composed of 36 units of instrument A and 24 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=4.92% 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=4.98% p.a.

Answer

a.

4.765 years

b.

5.651 years

c.

2.383 years

d.

2.825 years