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 2012 to create this portfolio and this portfolio is composed of 40 units of instrument A and 35 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 = 4.01% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.

(a) Calculate the current price of instrument A per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ =3.92% p.a.

a. 48.1633

b. 49.7194

c. 50.6939

d. 69.1565