Question

A $18000 bond redeemable at par on October 25, 2016 is purchased on August 25, 2007. Interest is 7.9% payable semi-annually and the yield is 6.8% compounded semi-annually.

(a) What is the cash price?

(b) What is the accrued interest?

(c) What is the quoted price?

Answer 1

Solution:

We know that :

Cash Price = Quoted Price + Accrued Interest (Since the last Coupon Date) … equation 1)

The interest is paid semi annually i.e. on 1st July (for the last six months) and 1st Jan (for the next 6)

C) In order to calculate the Quoted price we have with us

Par Value = 18000 , Coupon 7.9% Semiannually , 6.8% semi annual yield , N = 9 * 2 = 18 semi annual periods

We use our BA II plus calculator to calculate the quoted price.

PV = ?? , N = 18 , I/Y = 6.8 , PMT = 1422, FV = 18000 . After entering the values we press CPT + PV

We get the quoted price as : 20,020.

b) Accrued interest :

Interest in accrued for July and 25 days in Aug i.e. Using the 30/180 convention , days for which interest is accrued is 45

AI (30/180 method) {Since coupon is paid semiannually} = 1422* (25/180) = 1422 * .1388 = 197.5

So the accrued interest comes out to be 197.5

a) From the equation 1

Cash Price = Quoted Price + Accrued Interest

= 20020 + 197.5 = 20217.5

So we get the cash price as 20217.5