Jenna bought a new car for \( \$ 29,000 \). She paid a \( 10 \% \) down payment and financed the remaining balance for 48 months with an APR of \( 4.5 \% \). Determine the monthly payment that Jenna pays. Round your answer to the nearest cent, if necessary. Formulas Answer

To determine the monthly payment that Jenna pays, we can use the formula for calculating monthly payments on a loan: \[ \text{Monthly Payment} = \frac{\text{Loan Amount} \times \text{APR} \times (1 + \text{APR})^{n}}{(1 + \text{APR})^{n} - 1} \] where: - Loan Amount is the amount borrowed (in this case, the remaining balance after the down payment), - APR is the annual percentage rate (in decimal form), - n is the number of payments (in this case, 48 months). First, let's calculate the remaining balance after the down payment: \[ \text{Remaining Balance} = \text{Loan Amount} - \text{Down Payment} \] Given: - Loan Amount = $29,000 - Down Payment = 10% of $29,000 = 0.10 * $29,000 = $2,900 \[ \text{Remaining Balance} = $29,000 - $2,900 = $26,100 \] Now, we can calculate the monthly payment using the formula above. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(29000\times 0.045\left(1+0.045\right)^{48}\right)}{\left(\left(1+0.045\right)^{48}-1\right)}\) - step1: Remove the parentheses: \(\frac{29000\times 0.045\left(1+0.045\right)^{48}}{\left(1+0.045\right)^{48}-1}\) - step2: Add the numbers: \(\frac{29000\times 0.045\times 1.045^{48}}{\left(1+0.045\right)^{48}-1}\) - step3: Add the numbers: \(\frac{29000\times 0.045\times 1.045^{48}}{1.045^{48}-1}\) - step4: Convert the expressions: \(\frac{29000\times 0.045\left(\frac{209}{200}\right)^{48}}{1.045^{48}-1}\) - step5: Convert the expressions: \(\frac{29000\times 0.045\left(\frac{209}{200}\right)^{48}}{\left(\frac{209}{200}\right)^{48}-1}\) - step6: Multiply: \(\frac{1305\times \frac{209^{48}}{200^{48}}}{\left(\frac{209}{200}\right)^{48}-1}\) - step7: Subtract the numbers: \(\frac{1305\times \frac{209^{48}}{200^{48}}}{\frac{209^{48}-200^{48}}{200^{48}}}\) - step8: Evaluate the power: \(\frac{\frac{261\times 209^{48}}{5^{95}\times 8^{48}}}{\frac{209^{48}-200^{48}}{200^{48}}}\) - step9: Multiply by the reciprocal: \(\frac{261\times 209^{48}}{5^{95}\times 8^{48}}\times \frac{200^{48}}{209^{48}-200^{48}}\) - step10: Rewrite the expression: \(\frac{261\times 209^{48}}{5^{95}\times 8^{48}}\times \frac{25^{48}\times 8^{48}}{209^{48}-200^{48}}\) - step11: Rewrite the expression: \(\frac{261\times 209^{48}}{5^{95}\times 8^{48}}\times \frac{5^{96}\times 8^{48}}{209^{48}-200^{48}}\) - step12: Reduce the numbers: \(261\times 209^{48}\times \frac{5}{209^{48}-200^{48}}\) - step13: Multiply: \(\frac{261\times 209^{48}\times 5}{209^{48}-200^{48}}\) - step14: Multiply: \(\frac{1305\times 209^{48}}{209^{48}-200^{48}}\) The monthly payment that Jenna pays is approximately $1,484.47. Therefore, Jenna's monthly payment is $1,484.47.