What proceeds does shelly recieve

Question

Ron bought good from Shelly on Feb. 26, shell gave Ron time extension on his bill by accepting a 4800 6%, 155 day note. On May 18th Shelly discounted the note at Nose well bank at 11%. What proceeds does Shelly receive

Answer 1

To find the proceeds Shelly receives, we need to calculate the maturity value of the note and then subtract the bank's discount based on the remaining time.

1. Calculate the Maturity Value

First, find the interest earned over the full 155 days.

1. Principal: $4,800$
2. Interest Rate: $6\%$ (0.06)
3. Time: $155/360$ days (assuming a standard 360-day bank year)

$$Interest = 4800 \times 0.06 \times \frac{155}{360} = 124$$

$$Maturity Value = 4800 + 124 = 4924$$

2. Determine the Discount Period

We need to find how many days are left on the note from the date it was discounted (May 18) to the maturity date.

1. Origin Date: Feb 26
2. Maturity Date: 155 days after Feb 26 is July 31.
3. Discount Date: May 18
4. Days Remaining (May 18 to July 31):
5. Remaining in May: $31 - 18 = 13$ days
6. June: $30$ days
7. July: $31$ days
8. Total Discount Period: $13 + 30 + 31 = 74$ days

3. Calculate the Bank Discount

The bank takes its $11\%$ cut from the Maturity Value for the remaining $74$ days.

1. Maturity Value: $4,924$
2. Discount Rate: $11\%$ (0.11)
3. Time Remaining: $74/360$

$$Bank Discount = 4924 \times 0.11 \times \frac{74}{360} \approx 111.34$$

4. Calculate the Final Proceeds

Subtract the bank's discount from the maturity value to see what Shelly actually takes home.

$$Proceeds = 4924 - 111.34 = 4812.66$$

Shelly receives $4,812.66.