You want to buy a car. The loan amount will be \( \$ 30,000 \). The company is offering a \( 2 \% \) interest rate for 60 months ( 5 years). What will your monthly payments be? \( \$ \) Question Help: D Post to forum

To calculate the monthly payments for a car loan, we can use the formula for monthly payments on a loan: \[ M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \] Where: - \( M \) is the monthly payment - \( P \) is the principal amount (the loan amount) - \( r \) is the monthly interest rate - \( n \) is the number of payments (the number of months) Given: - Loan amount (\( P \)) = $30,000 - Interest rate = 2% per annum - Loan duration = 5 years = 60 months First, we need to convert the annual interest rate to a monthly interest rate: \[ r = \frac{2\%}{12} = \frac{0.02}{12} = 0.0016667 \] Now, we can substitute the values into the formula to calculate the monthly payment. Calculate the value by following steps: - step0: Calculate: \(\frac{30000\times 0.0016667\left(1+0.0016667\right)^{60}}{\left(\left(1+0.0016667\right)^{60}-1\right)}\) - step1: Remove the parentheses: \(\frac{30000\times 0.0016667\left(1+0.0016667\right)^{60}}{\left(1+0.0016667\right)^{60}-1}\) - step2: Add the numbers: \(\frac{30000\times 0.0016667\times 1.0016667^{60}}{\left(1+0.0016667\right)^{60}-1}\) - step3: Add the numbers: \(\frac{30000\times 0.0016667\times 1.0016667^{60}}{1.0016667^{60}-1}\) - step4: Convert the expressions: \(\frac{30000\times 0.0016667\left(\frac{10016667}{10000000}\right)^{60}}{1.0016667^{60}-1}\) - step5: Convert the expressions: \(\frac{30000\times 0.0016667\left(\frac{10016667}{10000000}\right)^{60}}{\left(\frac{10016667}{10000000}\right)^{60}-1}\) - step6: Multiply: \(\frac{\frac{50001\times 10016667^{60}}{10^{423}}}{\left(\frac{10016667}{10000000}\right)^{60}-1}\) - step7: Subtract the numbers: \(\frac{\frac{50001\times 10016667^{60}}{10^{423}}}{\frac{10016667^{60}-10000000^{60}}{10000000^{60}}}\) - step8: Multiply by the reciprocal: \(\frac{50001\times 10016667^{60}}{10^{423}}\times \frac{10000000^{60}}{10016667^{60}-10000000^{60}}\) - step9: Rewrite the expression: \(\frac{50001\times 10016667^{60}}{10^{423}}\times \frac{10^{420}}{10016667^{60}-10000000^{60}}\) - step10: Reduce the numbers: \(\frac{50001\times 10016667^{60}}{10^{3}}\times \frac{1}{10016667^{60}-10000000^{60}}\) - step11: Multiply the fractions: \(\frac{50001\times 10016667^{60}}{10^{3}\left(10016667^{60}-10000000^{60}\right)}\) - step12: Multiply: \(\frac{50001\times 10016667^{60}}{1000\times 10016667^{60}-10^{423}}\) The monthly payment for the car loan will be approximately $525.83.