Not yet answered Points out of 10.00 P Flag question Marleen purchases a patio set costing \( \$ 2,430 \) by taking out an \( 12.5 \% \) add-on installment loan. The loan requires a \( 20 \% \) down payment and equal monthly payments for 3 years. How much are Mariann's monthly payments? Select one: a. \( \$ 82.67 \) b. \( \$ 74.25 \) c. \( \$ 125.33 \) d. \( \$ 96.49 \)

To find Marleen's monthly payments for the patio set, we can follow these steps: 1. **Calculate the down payment**: The down payment is \( 20\% \) of the total cost of the patio set. 2. **Determine the loan amount**: Subtract the down payment from the total cost to find out how much Marleen needs to borrow. 3. **Calculate the total interest**: The loan has a \( 12.5\% \) add-on interest rate, which means we need to calculate the total interest on the loan amount. 4. **Calculate the total amount to be repaid**: Add the loan amount to the total interest to find out how much Marleen will repay in total. 5. **Determine the monthly payments**: Divide the total amount to be repaid by the number of months in the loan term (3 years = 36 months). Let's perform these calculations step by step. ### Step 1: Calculate the down payment \[ \text{Down Payment} = 0.20 \times 2430 \] ### Step 2: Determine the loan amount \[ \text{Loan Amount} = 2430 - \text{Down Payment} \] ### Step 3: Calculate the total interest The total interest for an add-on loan is calculated as: \[ \text{Total Interest} = \text{Loan Amount} \times 0.125 \] ### Step 4: Calculate the total amount to be repaid \[ \text{Total Amount to be Repaid} = \text{Loan Amount} + \text{Total Interest} \] ### Step 5: Determine the monthly payments \[ \text{Monthly Payments} = \frac{\text{Total Amount to be Repaid}}{36} \] Now, let's perform these calculations. 1. Calculate the down payment. 2. Calculate the loan amount. 3. Calculate the total interest. 4. Calculate the total amount to be repaid. 5. Calculate the monthly payments. I'll perform these calculations now. Calculate the value by following steps: - step0: Calculate: \(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\) - step1: Multiply the numbers: \(\left(2430-486\right)\times 0.125\) - step2: Subtract the numbers: \(1944\times 0.125\) - step3: Multiply the numbers: \(243\) Calculate or simplify the expression \( 2430 - (0.20 * 2430) \). Calculate the value by following steps: - step0: Calculate: \(2430-\left(0.2\times 2430\right)\) - step1: Multiply the numbers: \(2430-486\) - step2: Subtract the numbers: \(1944\) Calculate or simplify the expression \( 0.20 * 2430 \). Calculate the value by following steps: - step0: Calculate: \(0.2\times 2430\) - step1: Multiply the numbers: \(486\) Calculate or simplify the expression \( (2430 - (0.20 * 2430)) + ((2430 - (0.20 * 2430)) * 0.125) \). Calculate the value by following steps: - step0: Calculate: \(\left(2430-\left(0.2\times 2430\right)\right)+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)\) - step1: Multiply the numbers: \(\left(2430-486\right)+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)\) - step2: Subtract the numbers: \(1944+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)\) - step3: Multiply the numbers: \(1944+\left(\left(2430-486\right)\times 0.125\right)\) - step4: Subtract the numbers: \(1944+\left(1944\times 0.125\right)\) - step5: Multiply the numbers: \(1944+243\) - step6: Add the numbers: \(2187\) Calculate or simplify the expression \( ((2430 - (0.20 * 2430)) + ((2430 - (0.20 * 2430)) * 0.125)) / 36 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\left(2430-\left(0.2\times 2430\right)\right)+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)\right)}{36}\) - step1: Remove the parentheses: \(\frac{\left(2430-\left(0.2\times 2430\right)\right)+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)}{36}\) - step2: Multiply the numbers: \(\frac{\left(2430-486\right)+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)}{36}\) - step3: Subtract the numbers: \(\frac{1944+\left(\left(2430-\left(0.2\times 2430\right)\right)\times 0.125\right)}{36}\) - step4: Multiply the numbers: \(\frac{1944+\left(\left(2430-486\right)\times 0.125\right)}{36}\) - step5: Subtract the numbers: \(\frac{1944+\left(1944\times 0.125\right)}{36}\) - step6: Multiply the numbers: \(\frac{1944+243}{36}\) - step7: Add the numbers: \(\frac{2187}{36}\) - step8: Reduce the fraction: \(\frac{243}{4}\) Let's summarize the calculations step by step: 1. **Down Payment**: \[ \text{Down Payment} = 0.20 \times 2430 = 486 \] 2. **Loan Amount**: \[ \text{Loan Amount} = 2430 - 486 = 1944 \] 3. **Total Interest**: \[ \text{Total Interest} = 1944 \times 0.125 = 243 \] 4. **Total Amount to be Repaid**: \[ \text{Total Amount to be Repaid} = 1944 + 243 = 2187 \] 5. **Monthly Payments**: \[ \text{Monthly Payments} = \frac{2187}{36} \approx 60.75 \] Now, let's compare this result with the options provided: - a. \( \$ 82.67 \) - b. \( \$ 74.25 \) - c. \( \$ 125.33 \) - d. \( \$ 96.49 \) None of the options match the calculated monthly payment of \( \$ 60.75 \). It seems there might be a misunderstanding or miscalculation in the options provided. Please double-check the problem statement or the options given. If you have any further questions or need clarification, feel free to ask!