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Jackson decided to take out a car loan for the next three years. The car is selling at $39,000 with a down payment of $12,000. The car dealership provides Jackson with the option of repaying the loan in equal instalments at the end of each month, at an interest rate of 22% p.a. compounding monthly. Calculate the amount of money Jackson needs to pay each month and round your answer to 2 decimal places.

Question

Jackson decided to take out a car loan for the next three years. The car is selling at 39,000withadownpaymentof39,000 with a down payment of 12,000. The car dealership provides Jackson with the option of repaying the loan in equal instalments at the end of each month, at an interest rate of 22% p.a. compounding monthly. Calculate the amount of money Jackson needs to pay each month and round your answer to 2 decimal places.

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Solution

To calculate the monthly payment, we first need to calculate the loan amount, which is the selling price of the car minus the down payment.

  1. Calculate the loan amount: Loan amount = Selling price - Down payment Loan amount = 39,000−39,000 - 12,000 = $27,000

  2. Next, we need to calculate the monthly interest rate. The annual interest rate is 22%, but it compounds monthly, so we divide it by 12. Monthly interest rate = Annual interest rate / 12 Monthly interest rate = 22% / 12 = 1.83%

  3. Convert the percentage to a decimal by dividing by 100: Monthly interest rate = 1.83 / 100 = 0.0183

  4. The formula to calculate the monthly payment for a loan is: P = [r*PV] / [1 - (1 + r)^-n] where: P = monthly payment r = monthly interest rate PV = present value, i.e., the loan amount n = total number of payments, i.e., the loan term in months

  5. Substituting the values into the formula: P = [0.0183 * 27,000]/[1−(1+0.0183)−36]P=27,000] / [1 - (1 + 0.0183)^-36] P = 494.10 / 0.7047 P = $701.07

So, Jackson needs to pay approximately $701.07 each month.

This problem has been solved

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