Okay, let's walk through this step-by-step to understand how these interest earned amounts are calculated:
1) There are 2 coupon payment dates: March 1 (3/1) and September 1 (9/1). So the reference period is from 3/1 to 9/1.
2) In this reference period, there are 184 total days (9/1 - 3/1 = 184 days).
3) The coupon rate is 8% and the bond principal is $100. So each semi-annual coupon payment is $4 (0.08 * $100 / 2).
To calculate the interest earned from 3/1 to 7/3:
(Actual / Actual) method:
* There are actually 124 days between 3/1 and 7/3.
* So the interest earned = (124 / 184) * $4 = $2.6957
(30 / 360) method:
* We assume each month has 30 days and there are 360 days in a year.
* From 3/1 to 7/3 is 4 months and 2 days. 4 months * 30 days/month = 120 days. 2 days = 2 days. So 120 + 2 = 122 days.
* 122 / 360 = 0.3389. So the interest earned = 0.3389 * $4 = $2.7111
(Actual/360) method:
* Although there are actually 124 days, we calculate as if each month has 30 days.
* So from 3/1 to 7/3 is 4 months. 4 months * 30 days/month = 120 days.
* 120 / 180 days in 6 months = 0.667
* So the interest earned = 0.667 * $4 = $2.7556
Does this help explain the calculations? Let me know if you have any other questions!