I am confused as 2 methods give different answers. The difference lies in the "to the power" numbers for discounting.
Example: 2 year semi annual bond (4 periods), $1m annual Coupon Payment, 5% Yield (forget about repayment of principal for simplicity)
Standard formula for discounting coupon payments:
[0.5 * $1m / (1.025)^1] + [0.5 * $1m / (1.025)^2] + [0.5 * $1m / (1.025)^3] + [0.5 * $1m / (1.025)^4] $
ie 4 payments, all discounted with n going from 1 to 4, and cash flow and yield have been halved to £0.5m and 2.5%.
BUT
See Erik Banks' book: "Finance the basics" bottom of page 70 under formula 3.7. It is in Googlebooks: type "time horizon divided by fractional period" into Google
Everything is the same except the values of n (the power that 1.025 is raised).
In his version, instead of being 1 to 4 respectively, n
is 1/2, 2/2, 3/2, 4/2
So each n
is divided by 2, because there are 2 payments each year.