Ron bought goods from shelly katz. On may 8, shelly gave ron a time extension on his bill by accepting a $3000, 8%, 180 day note. On august 16, shelly discounted the note at Roseville bank at 9% what proceeds does shelly rerceive?

To find out the proceeds that Shelly receives after discounting the note at Roseville bank, we need to calculate the discounted value of the note.

First, let's find the interest on the note for the given time period. The formula to calculate simple interest is:

I = P * r * t

Where:
I = Interest
P = Principal amount (in this case, $3000)
r = Interest rate (8% or 0.08)
t = Time in years (180 days / 365)

Let's calculate the interest on the note:
I = 3000 * 0.08 * (180/365)
I ≈ 118.90 (rounded to 2 decimal places)

Now, let's calculate the remaining balance on the note after deducting the interest:
Remaining balance = Principal - Interest
Remaining balance = $3000 - $118.90
Remaining balance ≈ $2881.10

Next, we need to calculate the discounted value of the note. The formula to calculate the discounted value is:

Discounted value = Remaining balance * (1 - r * t')

Where:
t' = Time in years from the date of discounting till the maturity date (August 16 to the maturity date)

Let's calculate the time in years (t'):
t' = (August 16 - May 8) / 365

Note: Since the given date doesn't contain the year, we'll assume the year is the current year.

t' = (August 16 - May 8) / 365
t' = (8 - 5) / 365
t' ≈ 0.0082 (rounded to 4 decimal places)

Now, let's calculate the discounted value:
Discounted value = $2881.10 * (1 - 0.09 * 0.0082)
Discounted value ≈ $2855.35 (rounded to 2 decimal places)

Therefore, Shelly receives $2855.35 as proceeds after discounting the note at Roseville bank.