You want to take out a \( \$ 222,000 \) mortgage (home loan). The interest rate on the loan is \( 4.2 \% \), and the loan is for 30 years. Your monthly payments are \( \$ 1,085.62 \). How much will still be owed after making payments for 10 years? \( \$ \) How much will still be owed after making payments for 20 years? \( \$ \) How much will still be owed after making payments for 25 years? \$ Round your answers to the nearest dollar. Question Help:

To calculate how much will still be owed after making payments for 10 years, 20 years, and 25 years, we can use the formula for the remaining balance of a mortgage: \[ \text{Remaining Balance} = \text{Principal} \times \left(1 + \frac{\text{Interest Rate}}{12}\right)^{12 \times \text{Number of Years}} \] Given: - Principal = $222,000 - Interest Rate = 4.2% = 0.042 - Number of Years = 10, 20, and 25 years Let's calculate the remaining balance for each scenario: Calculate the value by following steps: - step0: Calculate: \(222000\left(1+\frac{0.042}{12}\right)^{12\times 10}\) - step1: Divide the terms: \(222000\left(1+\frac{7}{2000}\right)^{12\times 10}\) - step2: Add the numbers: \(222000\left(\frac{2007}{2000}\right)^{12\times 10}\) - step3: Multiply the numbers: \(222000\left(\frac{2007}{2000}\right)^{120}\) - step4: Simplify: \(222000\times \frac{2007^{120}}{2000^{120}}\) - step5: Rewrite the expression: \(2000\times 111\times \frac{2007^{120}}{2000^{120}}\) - step6: Reduce the numbers: \(111\times \frac{2007^{120}}{2000^{119}}\) - step7: Multiply: \(\frac{111\times 2007^{120}}{2000^{119}}\) Calculate or simplify the expression \( 222000*(1 + 0.042/12)^(12*20) \). Calculate the value by following steps: - step0: Calculate: \(222000\left(1+\frac{0.042}{12}\right)^{12\times 20}\) - step1: Divide the terms: \(222000\left(1+\frac{7}{2000}\right)^{12\times 20}\) - step2: Add the numbers: \(222000\left(\frac{2007}{2000}\right)^{12\times 20}\) - step3: Multiply the numbers: \(222000\left(\frac{2007}{2000}\right)^{240}\) - step4: Simplify: \(222000\times \frac{2007^{240}}{2000^{240}}\) - step5: Rewrite the expression: \(2000\times 111\times \frac{2007^{240}}{2000^{240}}\) - step6: Reduce the numbers: \(111\times \frac{2007^{240}}{2000^{239}}\) - step7: Multiply: \(\frac{111\times 2007^{240}}{2000^{239}}\) Calculate or simplify the expression \( 222000*(1 + 0.042/12)^(12*25) \). Calculate the value by following steps: - step0: Calculate: \(222000\left(1+\frac{0.042}{12}\right)^{12\times 25}\) - step1: Divide the terms: \(222000\left(1+\frac{7}{2000}\right)^{12\times 25}\) - step2: Add the numbers: \(222000\left(\frac{2007}{2000}\right)^{12\times 25}\) - step3: Multiply the numbers: \(222000\left(\frac{2007}{2000}\right)^{300}\) - step4: Simplify: \(222000\times \frac{2007^{300}}{2000^{300}}\) - step5: Rewrite the expression: \(2000\times 111\times \frac{2007^{300}}{2000^{300}}\) - step6: Reduce the numbers: \(111\times \frac{2007^{300}}{2000^{299}}\) - step7: Multiply: \(\frac{111\times 2007^{300}}{2000^{299}}\) The remaining balance after making payments for 10 years is approximately $337,628. The remaining balance after making payments for 20 years is approximately $513,480. The remaining balance after making payments for 25 years is approximately $633,236.