Question

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 28 units of instrument A and 50 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 = 3.93% 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 =2.96% p.a.

Select one:

a. 59.7976

b. 75.6434

c. 58.9255

d. 57.4510

Answer 1

b. 75.6434

Price of the zero coupon bond is the present value of its par value

Which is

Par value /(1+rate)^n

Where

r=2.96%/2

n= 19

Price of the bond= 100/ (1+2.96%/2)^19

=100/ 1.321991651

=75.64344291