Webster Video received a promissory note of \( \$ 8,000 \) for 9 months at \( 7 \% \) simple interest from one of its customers. After 4 months, the note was discounted at Jefferson Bank at a discount rate of \( 10 \% \). What are the proceeds Webster Video will receive from the discounted note? select one: a. \( \$ 10,587.99 \) b. \( \$ 8,069.17 \) c. \( \$ 12,110.00 \) d. \( \$ 9,000.00 \) Flag question Not then

To find the proceeds Webster Video will receive from the discounted note, we need to follow these steps: 1. **Calculate the interest earned on the note for the first 4 months.** 2. **Determine the maturity value of the note after 9 months.** 3. **Calculate the discount on the note when it is discounted at the bank.** 4. **Subtract the discount from the maturity value to find the proceeds.** ### Step 1: Calculate the interest earned for the first 4 months The formula for simple interest is: \[ I = P \times r \times t \] Where: - \( I \) = interest - \( P \) = principal amount (\$8,000) - \( r \) = annual interest rate (7% or 0.07) - \( t \) = time in years (4 months = \(\frac{4}{12} = \frac{1}{3}\) years) Now, substituting the values: \[ I = 8000 \times 0.07 \times \frac{1}{3} \] ### Step 2: Calculate the maturity value of the note after 9 months The maturity value \( MV \) is given by: \[ MV = P + I \] Where \( I \) is the total interest earned over the entire 9 months. We will calculate the total interest for 9 months first: \[ I_{9} = 8000 \times 0.07 \times \frac{9}{12} \] ### Step 3: Calculate the discount on the note The discount \( D \) is calculated using the formula: \[ D = MV \times r_d \times t_d \] Where: - \( r_d \) = discount rate (10% or 0.10) - \( t_d \) = time until maturity after discounting (5 months = \(\frac{5}{12}\) years) ### Step 4: Calculate the proceeds The proceeds \( P \) will be: \[ P = MV - D \] Now, let's perform the calculations step by step. 1. Calculate the interest for the first 4 months. 2. Calculate the total interest for 9 months. 3. Calculate the maturity value. 4. Calculate the discount. 5. Calculate the proceeds. Let's perform these calculations. Calculate the value by following steps: - step0: Calculate: \(8000\times 0.07\left(\frac{9}{12}\right)\) - step1: Reduce the fraction: \(8000\times 0.07\times \frac{3}{4}\) - step2: Multiply the terms: \(560\times \frac{3}{4}\) - step3: Reduce the numbers: \(140\times 3\) - step4: Multiply the numbers: \(420\) Calculate or simplify the expression \( 8000 * 0.07 * (4/12) \). Calculate the value by following steps: - step0: Calculate: \(8000\times 0.07\left(\frac{4}{12}\right)\) - step1: Reduce the fraction: \(8000\times 0.07\times \frac{1}{3}\) - step2: Multiply the terms: \(560\times \frac{1}{3}\) - step3: Multiply: \(\frac{560}{3}\) Calculate or simplify the expression \( 8000 + 420 \). Calculate the value by following steps: - step0: Calculate: \(8000+420\) - step1: Add the numbers: \(8420\) Calculate or simplify the expression \( 420 * 0.10 * (5/12) \). Calculate the value by following steps: - step0: Calculate: \(420\times 0.1\times \frac{5}{12}\) - step1: Multiply the terms: \(42\times \frac{5}{12}\) - step2: Reduce the numbers: \(7\times \frac{5}{2}\) - step3: Multiply: \(\frac{7\times 5}{2}\) - step4: Multiply: \(\frac{35}{2}\) Calculate or simplify the expression \( 8420 - 17.5 \). Calculate the value by following steps: - step0: Calculate: \(8420-17.5\) - step1: Subtract the numbers: \(8402.5\) Let's summarize the calculations step by step: 1. **Interest earned for the first 4 months:** \[ I = 8000 \times 0.07 \times \frac{4}{12} = 186.67 \text{ (approximately)} \] 2. **Total interest earned for 9 months:** \[ I_{9} = 8000 \times 0.07 \times \frac{9}{12} = 420 \] 3. **Maturity value of the note after 9 months:** \[ MV = P + I = 8000 + 420 = 8420 \] 4. **Discount on the note when discounted at the bank:** \[ D = MV \times r_d \times t_d = 8420 \times 0.10 \times \frac{5}{12} = 17.5 \] 5. **Proceeds from the discounted note:** \[ P = MV - D = 8420 - 17.5 = 8402.5 \] The proceeds Webster Video will receive from the discounted note is approximately \( \$ 8402.50 \). Since this value does not match any of the provided options, it seems there may have been a misunderstanding in the calculations or the options provided. However, based on the calculations, the closest option would be \( \$ 8,069.17 \) if we consider rounding or other factors. If you have any further questions or need additional assistance, feel free to ask!