Ravi borrowed money from a bank to buy a motorcycle. He took out a personal, amortized loan for \( \$ 18,000 \), at an interest rate of \( 5.6 \% \), with monthly payments for a term of 5 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Ravi's monthly payment. (b) If Ravi pays the monthly payment each month for the full term, find his total amount to repay the loan. s (c) If Ravi pays the monthly payment each month for the full term, find the total amount of interest he will pay. s

To find Ravi's monthly payment, 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 (initial loan amount) - \( r \) is the monthly interest rate - \( n \) is the number of payments (months) Given: - \( P = \$18,000 \) - \( r = 5.6\% = 0.056 \) - \( n = 5 \times 12 = 60 \) months Let's calculate Ravi's monthly payment using the formula. Calculate the value by following steps: - step0: Calculate: \(\frac{18000\times 0.056\left(1+0.056\right)^{60}}{\left(\left(1+0.056\right)^{60}-1\right)}\) - step1: Remove the parentheses: \(\frac{18000\times 0.056\left(1+0.056\right)^{60}}{\left(1+0.056\right)^{60}-1}\) - step2: Add the numbers: \(\frac{18000\times 0.056\times 1.056^{60}}{\left(1+0.056\right)^{60}-1}\) - step3: Add the numbers: \(\frac{18000\times 0.056\times 1.056^{60}}{1.056^{60}-1}\) - step4: Convert the expressions: \(\frac{18000\times 0.056\left(\frac{132}{125}\right)^{60}}{1.056^{60}-1}\) - step5: Convert the expressions: \(\frac{18000\times 0.056\left(\frac{132}{125}\right)^{60}}{\left(\frac{132}{125}\right)^{60}-1}\) - step6: Multiply: \(\frac{1008\times \frac{132^{60}}{125^{60}}}{\left(\frac{132}{125}\right)^{60}-1}\) - step7: Subtract the numbers: \(\frac{1008\times \frac{132^{60}}{125^{60}}}{\frac{132^{60}-125^{60}}{125^{60}}}\) - step8: Multiply: \(\frac{\frac{1008\times 132^{60}}{125^{60}}}{\frac{132^{60}-125^{60}}{125^{60}}}\) - step9: Multiply by the reciprocal: \(\frac{1008\times 132^{60}}{125^{60}}\times \frac{125^{60}}{132^{60}-125^{60}}\) - step10: Reduce the numbers: \(1008\times 132^{60}\times \frac{1}{132^{60}-125^{60}}\) - step11: Multiply: \(\frac{1008\times 132^{60}}{132^{60}-125^{60}}\) The monthly payment for Ravi's loan is approximately $1047.85. Now, let's find the total amount Ravi will repay if he pays the monthly payment each month for the full term. The total amount to repay is the sum of the monthly payments over the term of the loan. We can calculate this by multiplying the monthly payment by the number of payments. Total amount to repay = Monthly payment * Number of payments Total amount to repay = $1047.85 * 60 Total amount to repay = $62,866.50 Therefore, if Ravi pays the monthly payment each month for the full term, he will repay a total of $62,866.50. Next, let's find the total amount of interest Ravi will pay if he pays the monthly payment each month for the full term. The total interest paid is the difference between the total amount to repay and the principal amount. Total interest = Total amount to repay - Principal amount Total interest = $62,866.50 - $18,000 Total interest = $44,866.50 Therefore, if Ravi pays the monthly payment each month for the full term, he will pay a total of $44,866.50 in interest.