If JAB Consulting received a promissory note of \( \$ 13,500 \) at \( 7 \% \) simple interest for 15 5 months from one of its customers. After 6 months, Grove Isle Bank discounted the note at a discount rate of \( 4 \% \) Calculate the proceeds (in \( \$ \) ) that JAB Consulting will receive from the discounted note. (Round your answer to the nearest cent.)

To solve the problem, we will follow these steps: 1. **Calculate the interest earned on the promissory note for the first 6 months.** 2. **Determine the maturity value of the note after 15 months.** 3. **Calculate the discount on the note when it is discounted at the bank after 6 months.** 4. **Calculate the proceeds that JAB Consulting will receive from the discounted note.** ### Step 1: Calculate the interest earned for the first 6 months The formula for simple interest is given by: \[ I = P \times r \times t \] Where: - \( I \) = interest - \( P \) = principal amount (\$13,500) - \( r \) = interest rate (7% or 0.07) - \( t \) = time in years (6 months = 0.5 years) Now, substituting the values: \[ I = 13500 \times 0.07 \times 0.5 \] ### Step 2: Determine the maturity value of the note after 15 months The maturity value \( MV \) is calculated as: \[ MV = P + I \] Where \( I \) is the interest earned over the entire period of 15 months (1.25 years). First, we need to calculate the total interest for 15 months: \[ I_{total} = 13500 \times 0.07 \times 1.25 \] Then, we can find the maturity value: \[ MV = 13500 + I_{total} \] ### Step 3: Calculate the discount on the note The discount \( D \) is calculated using the formula: \[ D = MV \times d \times t \] Where: - \( d \) = discount rate (4% or 0.04) - \( t \) = time until maturity after discounting (15 months - 6 months = 9 months = 0.75 years) Now, substituting the values: \[ D = MV \times 0.04 \times 0.75 \] ### Step 4: Calculate the proceeds The proceeds \( P \) that JAB Consulting will receive is given by: \[ P = MV - D \] Now, let's perform the calculations step by step. ### Calculating the interest for the first 6 months \[ I = 13500 \times 0.07 \times 0.5 \] ### Calculating the total interest for 15 months \[ I_{total} = 13500 \times 0.07 \times 1.25 \] ### Calculating the maturity value \[ MV = 13500 + I_{total} \] ### Calculating the discount \[ D = MV \times 0.04 \times 0.75 \] ### Calculating the proceeds \[ P = MV - D \] Now, I will perform these calculations. Calculate the value by following steps: - step0: Calculate: \(13500\times 0.07\times 0.5\) - step1: Multiply the terms: \(945\times 0.5\) - step2: Multiply the numbers: \(472.5\) Calculate or simplify the expression \( 13500 * 0.07 * 1.25 \). Calculate the value by following steps: - step0: Calculate: \(13500\times 0.07\times 1.25\) - step1: Multiply the terms: \(945\times 1.25\) - step2: Multiply the numbers: \(1181.25\) Calculate or simplify the expression \( 13500 + 1181.25 \). Calculate the value by following steps: - step0: Calculate: \(13500+1181.25\) - step1: Add the numbers: \(14681.25\) Calculate or simplify the expression \( MV * 0.04 * 0.75 \). Simplify the expression by following steps: - step0: Solution: \(MV\times 0.04\times 0.75\) - step1: Multiply the terms: \(MV\times 0.03\) - step2: Reorder the terms: \(0.03MV\) Calculate or simplify the expression \( 14681.25 * 0.04 * 0.75 \). Calculate the value by following steps: - step0: Calculate: \(14681.25\times 0.04\times 0.75\) - step1: Multiply the terms: \(587.25\times 0.75\) - step2: Multiply the numbers: \(440.4375\) Calculate or simplify the expression \( 14681.25 - 440.4375 \). Calculate the value by following steps: - step0: Calculate: \(14681.25-440.4375\) - step1: Subtract the numbers: \(14240.8125\) Let's summarize the calculations step by step: 1. **Interest earned for the first 6 months:** \[ I = 13500 \times 0.07 \times 0.5 = 472.50 \] 2. **Total interest for 15 months:** \[ I_{total} = 13500 \times 0.07 \times 1.25 = 1181.25 \] 3. **Maturity value of the note after 15 months:** \[ MV = 13500 + 1181.25 = 14681.25 \] 4. **Discount on the note when discounted at the bank:** \[ D = MV \times 0.04 \times 0.75 = 14681.25 \times 0.04 \times 0.75 = 440.4375 \] 5. **Proceeds that JAB Consulting will receive from the discounted note:** \[ P = MV - D = 14681.25 - 440.4375 = 14240.8125 \] Finally, rounding to the nearest cent, the proceeds that JAB Consulting will receive from the discounted note is: \[ \boxed{14240.81} \]