Jackson decided to take out a car loan for the next three years. The car is selling at $36,000 with a down payment of $10,000. 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 24% 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 10,000. 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 24% p.a. compounding monthly. Calculate the amount of money Jackson needs to pay each month and round your answer to 2 decimal places.
Solution
First, we need to calculate the loan amount. The loan amount is the selling price of the car minus the down payment.
Loan amount = Selling price - Down payment Loan amount = 10,000 Loan amount = $26,000
Next, we need to calculate the monthly interest rate. The annual interest rate is 24%, and it is compounded monthly. Therefore, the monthly interest rate is the annual interest rate divided by 12.
Monthly interest rate = Annual interest rate / 12 Monthly interest rate = 24% / 12 Monthly interest rate = 2%
Now, we need to calculate the number of payments. The loan is for three years, and payments are made monthly. Therefore, the number of payments is 3 years times 12 months per year.
Number of payments = 3 years * 12 months/year Number of payments = 36 months
Finally, we can calculate the monthly payment using the formula for the monthly payment on a loan:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)
Monthly payment = (520 / (1 - 1.02^-36) Monthly payment = 938.57
Therefore, Jackson needs to pay approximately $938.57 each month.
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