# Day count conventions

• Day count defines the way in which interest is accrued over time. Day count conventions normally used in US are:
• Actual / actual->  treasury bonds
• 30 / 360->  corporate bonds
• Actual/360->  money market instruments
• The interest earned between two dates

Examples

• Actual / 360
• The interest price of a 91-day T-bill is 9%. Find the dollar amount of interest paid over the 91 day period and the corresponding rate of interest
• Dollar interest is $100*0.09*91/360 =$2.275
• Rate of interest = 2.275/(100-2.275) = 2.328 %
• Actual / Actual
• A treasury bond with face value $100 pays a semi-annual coupon of 12%. Coupon payment dates are Mar 1 and Sept 1. Find the interest earned between Mar 1 & July 3 • Reference period Mar 1 to Sept 1 is 184 days • Desired period is Mar 1 and July 3, is 124 days • Interest earned is 124/184*6 =$4.043
• 30 / 360
• A corporate bond with face value $100 pays a semi-annual coupon of 12%. Coupon payment dates are Mar 1 and Sept 1. Find the interest earned between Mar 1 & July 3 • Reference period Mar 1 to Sept 1 is 6 months with each month @30 days =180 days • Desired period is Mar 1 and July 3, is 4*30 + 2 = 122 days • Interest earned is 122/180*6 =$4.0666