On September 5, Sheffield Company Discounted at Sunshine Bank a 9000.00 (maturity value), 120-day note dated June 5th Sunshine's discounted rate was 9%. What proceeds did Sheffield Company Receive?

Answer 1

The company gets the 9,000 - interest paid up front
the interest paid is
9,000 (120 days/days in year) (.09)
now you did not say if you were using an exact year of 365 days or a bankers year of 360 days, which makes calculations easier. I will assume a full year of 365 days.
9,000 * (120/365) * .09 = 266.30
so the company would get
9,000 -266.30 = 8733.70
If we used a banker's 360 day year, 120 days is 1/3 year
interest = (9,000/3)*.09 = 270.00
and the company gets
9,000-270 = 8730
Note that the company gets less and the bank gets more using a "banker's year"

Now using the 8730 the company actually got with the banker's year, let's find out what the effective interest rate was. I know this was not asked but it is "interesting"
the company paid 270 for 8730 for 1/3 year
so the effective rate is
(270/8730)*3 = .093
or 9.3 percent, not 9 percent. Remember that at the bank desk :)

Answer 2

we are using 360 would this still be right the way you fugured it