A bond with an 8% coupon paid semi-annually on 15 January and 15 July each year is currently listed at an ask price of 102.50%. If you want to purchase this bond today, with today’s date as 15 August 2020, how much will you pay for one bond?  

Price payable = $103.16

Step-by-step explanation

Looking at the quantum of price %, thr face value can be assumed to be $100, since it is not given already.

The listed price or clean price is = 102.50% of face value i.e. listed price = 102.50% * $100 = $102.50

Now since the purchase date i.e. 15th August is not a coupon date, we need to pay the accrued interest for 1 month to the saller.

Since interest on bond is semiannual, we need to make it monthly. Which can be done as follows.

Let the monthly rate be = r

A semiannual period has 6 month therefore

(1+r)^6 = (1+8%/2)

(1+r)^6 = 1.04

r = 0.006558 or 0.6558%

i.e. accrued interest = $100 * 0.6558% = $0.66

Hence the total payable price = 102.50 + 0.66 = $103.16

Tutorial note: this interest inclusive price is called dirty price.