Your Office Supply has a \( \$ 42,500 \) line of credit that charges an annual percentage rate of prime rate plus \( 3 \% \). Their starting balance on March 1 was \( \$ 10,600 \). On March 5 they borrowed \( \$ 7,500 \). On March 14 the business made a payment of \( \$ 3,300 \), and on March 18 they borrowed \( \$ 5,300 \). If the current prime rate is \( 9 \% \), what is the new balance? Select one: O. \( \$ 26,100.00 \) ob. \( \$ 20,276.10 \) c. \( \$ 27,583.43 \) o d. \( \$ 18,400.29 \)

To find the new balance of Your Office Supply after the transactions and interest charges, we will follow these steps: 1. **Calculate the effective annual percentage rate (APR)**: - The prime rate is \( 9\% \). - The APR is \( 9\% + 3\% = 12\% \). 2. **Calculate the daily interest rate**: - The daily interest rate is calculated as: \[ \text{Daily Interest Rate} = \frac{12\%}{365} = \frac{0.12}{365} \approx 0.0003287671 \] 3. **Calculate the balance after each transaction and the interest accrued**: - Starting balance on March 1: \( B_0 = 10,600 \) - **March 5**: Borrowed \( 7,500 \) - New balance: \[ B_1 = B_0 + 7,500 = 10,600 + 7,500 = 18,100 \] - **March 14**: Payment of \( 3,300 \) - New balance: \[ B_2 = B_1 - 3,300 = 18,100 - 3,300 = 14,800 \] - **March 18**: Borrowed \( 5,300 \) - New balance: \[ B_3 = B_2 + 5,300 = 14,800 + 5,300 = 20,100 \] 4. **Calculate the interest accrued from March 1 to March 18**: - Days from March 1 to March 5: \( 4 \) days - Days from March 5 to March 14: \( 9 \) days - Days from March 14 to March 18: \( 4 \) days - Total days for interest calculation: \[ \text{Total Days} = 4 + 9 + 4 = 17 \] 5. **Calculate interest for each period**: - Interest from March 1 to March 5 on \( 10,600 \): \[ I_1 = B_0 \times \text{Daily Interest Rate} \times 4 = 10,600 \times 0.0003287671 \times 4 \] - Interest from March 5 to March 14 on \( 18,100 \): \[ I_2 = B_1 \times \text{Daily Interest Rate} \times 9 = 18,100 \times 0.0003287671 \times 9 \] - Interest from March 14 to March 18 on \( 14,800 \): \[ I_3 = B_2 \times \text{Daily Interest Rate} \times 4 = 14,800 \times 0.0003287671 \times 4 \] 6. **Calculate the total interest**: - Total interest \( I \): \[ I = I_1 + I_2 + I_3 \] 7. **Calculate the new balance**: - New balance: \[ \text{New Balance} = B_3 + I \] Now, let's perform the calculations step by step. ### Step 1: Calculate Interest for Each Period 1. **Interest from March 1 to March 5**: \[ I_1 = 10,600 \times 0.0003287671 \times 4 \] 2. **Interest from March 5 to March 14**: \[ I_2 = 18,100 \times 0.0003287671 \times 9 \] 3. **Interest from March 14 to March 18**: \[ I_3 = 14,800 \times 0.0003287671 \times 4 \] Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(18100\times \frac{3287671}{10000000000}\times 9\) - step1: Multiply the terms: \(\frac{595068451}{100000000}\times 9\) - step2: Multiply: \(\frac{595068451\times 9}{100000000}\) - step3: Multiply: \(\frac{5355616059}{100000000}\) Calculate or simplify the expression \( 10,600 * 0.0003287671 * 4 \). Calculate the value by following steps: - step0: Calculate: \(10600\times \frac{3287671}{10000000000}\times 4\) - step1: Multiply the terms: \(\frac{174246563}{50000000}\times 4\) - step2: Reduce the numbers: \(\frac{174246563}{12500000}\times 1\) - step3: Multiply: \(\frac{174246563}{12500000}\) Calculate or simplify the expression \( 14,800 * 0.0003287671 * 4 \). Calculate the value by following steps: - step0: Calculate: \(14800\times \frac{3287671}{10000000000}\times 4\) - step1: Multiply the terms: \(\frac{121643827}{25000000}\times 4\) - step2: Reduce the numbers: \(\frac{121643827}{6250000}\times 1\) - step3: Multiply: \(\frac{121643827}{6250000}\) Now we have calculated the interest for each period: 1. **Interest from March 1 to March 5**: \[ I_1 \approx 13.94 \] 2. **Interest from March 5 to March 14**: \[ I_2 \approx 53.56 \] 3. **Interest from March 14 to March 18**: \[ I_3 \approx 19.46 \] ### Step 2: Calculate Total Interest Now, we will sum these interest amounts to find the total interest \( I \): \[ I = I_1 + I_2 + I_3 \approx 13.94 + 53.56 + 19.46 \] Let's calculate the total interest. Calculate the value by following steps: - step0: Calculate: \(13.94+53.56+19.46\) - step1: Add the numbers: \(86.96\) The total interest \( I \) is approximately: \[ I \approx 86.96 \] ### Step 3: Calculate the New Balance Now, we will calculate the new balance using the last balance before interest and adding the total interest: \[ \text{New Balance} = B_3 + I = 20,100 + 86.96 \] Let's calculate the new balance. Calculate the value by following steps: - step0: Calculate: \(20100+86.96\) - step1: Add the numbers: \(20186.96\) The new balance after all transactions and interest is approximately: \[ \text{New Balance} \approx 20,186.96 \] ### Conclusion The closest option to the calculated new balance of \( \$ 20,186.96 \) is: - **Option b: \( \$ 20,276.10 \)** Thus, the new balance is approximately \( \$ 20,276.10 \).