Ron Prentice bought a goods from Shelly Katz. On May 8, Shelly gave Ron a time extension on his bill by accepting a 3000.00, 8%, 180-day note. On August 16, Shelly discounted the note at Roseville Bank at 9%. What proceeds does Shelly Receive? Please use 360 days and not 365
To calculate the proceeds that Shelly receives after discounting the note at Roseville Bank, we need to determine the maturity value of the note and the interest deducted by the bank.
First, let's calculate the maturity value of the note. The formula to calculate the maturity value is:
Maturity Value = Principal + Interest
Given:
Principal (P) = $3000.00
Rate of Interest (R) = 8% (expressed as a decimal, so 0.08)
Time (T) = 180 days
Number of days in a year (N) = 360
Using the formula for simple interest:
Interest (I) = P * R * T / N
Substituting the given values into the formula:
Interest (I) = $3000.00 * 0.08 * 180 / 360
Interest (I) = $120.00
Therefore, the maturity value is:
Maturity Value = Principal + Interest
Maturity Value = $3000.00 + $120.00
Maturity Value = $3120.00
Now, let's calculate the proceeds that Shelly receives after discounting the note at Roseville Bank. The formula to calculate the proceeds is:
Proceeds = Maturity Value - Discount
Given:
Rate of Discount (D) = 9% (expressed as a decimal, so 0.09)
Using the formula to calculate the discount:
Discount (DIS) = Maturity Value * D * T / N
Substituting the given values into the formula:
Discount (DIS) = $3120.00 * 0.09 * 79 / 360
Discount (DIS) = $68.60
Therefore, the proceeds that Shelly receives are:
Proceeds = Maturity Value - Discount
Proceeds = $3120.00 - $68.60
Proceeds = $3051.40
Hence, Shelly receives $3051.40 as proceeds after discounting the note at Roseville Bank.