Question

a) Consider a 5 1/8 bond, maturing 12/31/02 (coupon payment date is 06/30 and 12/31), 8 trading at 101:11 for settlement 8/12/02. Calculate accrued interest and invoice price (M=100,000).

b) Consider now a 5 1/2 bond, maturing 3/31/03, trading at 102:15 for settlement 8/12/02. Calculate accrued interest and invoice price (M=100,000).

Answer 1

Part A) Calculating Accrued Interest

Q1 . Accrued interest

• Last coupon payment = 30th June
• Settlement date = 12th August

Total time between settlement and last coupon payment = 30 ( July) +12 (August) = 42

Time between coupon payment = 180 days

(using 30/360 convention that is used for calculation in bond settlement)

Coupon payment = 5.125% Annual, Semi annual = 2.5625%

Coupon payment in dollars = face value * Coupon rate = 2.5625% * 100 = 2.5625

Accrued interest = time between settlement and last coupon payment / Time between coupon payment * interest payment = 42/180 * 2.5625 = 0.5979

In bond pricing quotation method (1/32) Acrrued Interest = .5979 *32/100 = .1913

Invoice price = Quote price + Acrrued interest = 101:11 + : 19 = 101:30

Q2. Dates are same but coupon payment has changed

Coupon = 5.5 annual and 5.5/2 = 2.75

Acrrued interest = 42/180 * 2.75 = 0.6416

In bond pricing quotation method (1/32) Acrrued Interest = .6416*32/100 = .20533

Invoice price = 102:15 + :20 = 102:35 (32+3) =103:03