Question

what rate of annual simple interest is equivalent to 9% per annum compounded semi-annually for 3 years

Answer 1

rate = (1.045)^2
= 1.092025

or 9.2025 %

since you want the annual simple interest, the 3 years is irrelevant, all we have to do is look at a 1 year period

Answer 2

looked at it again....

amount after 3 years at the compound interest
= 1.045^6
= 1.30226

so interest on $1 is .30226

using I = PRT
.30226 = 1(r)(3)
r = .10075

the annual simple interest is 10.075%

check:
Assume we have $100

amount after 3 years using the compound interest
= 300(1.045)^6 = 130.23

amount using simple interest of 10.075%
= 100 + 100(.10075)(3) = 130.23

YEAHHH