Question

Henry is planning to purchase a Treasury bond with a coupon rate of 3.02% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 3 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 2.39% p.a. compounded half-yearly.

Select one:

a. 107.8175

b. 109.3277

c. 109.3263

d. 109.11

Answer 1

Step 1: Value on 15 May 2018

Price = Half yearly coupen amount * PVAF (half yearly yield, number of half years) + Face value * PVIF (half yearly yield, number of half years)

        = [ 100 * 3.02% * 6/12 ] * PVAF (2.39%/2, 15*2 ) + 100 * PVIF (2.39%/2, 15*2 )

        = 1.51 * PVAF ( 1.195%, 30 ) + 100 * PVIF ( 1.195%, 30 )

        = 1.51 * [ 1/1.01195 + 1/1.01195² + ...... + 1/1.01195³⁰ ] + 100 * ( 1/1.01195³⁰ )

        = 37.8814 + 70.021

        = 107.9024

Step 2: Value on 3 May 2018 ( 12 days from 15th may 2018 )

Price = 107.9024 * [ 1/1.01195^{(12 / 182.5)} ] [ Explanation - Price of 15 th May 2018 is pulled to 12 days back at 3rd May 2018. Since rate is half yearly hence 182.5 days takes )

        = 107.9024 * 0.999219

        = 107.8175 Answer

Option A is correct