John Buys a used car costing $6000. He agrees to make payments at the end of each monthly period for four years. He pays 12% interest compounded monthly. What is the amount of each payment? Find the total amount of interest John pays on the loan.
To find the amount of each payment and the total amount of interest John pays on the loan, we can use the formula for calculating the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = present value of the loan (initial loan amount)
n = number of monthly payments
First, let's find the monthly interest rate. John's loan has 12% interest compounded monthly, so we need to convert the annual interest rate to a monthly rate.
r = (12% / 100) / 12 = 0.01
Next, let's calculate the present value (PV) of the loan, which is the initial loan amount of $6000.
Now, we need to determine the number of monthly payments. John will make payments for four years, which is 4 * 12 = 48 months.
Using the formula, we can calculate the monthly payment:
P = (0.01 * $6000) / (1 - (1 + 0.01)^(-48))
P = $144.32 (rounded to two decimal places)
Therefore, the amount of each payment is $144.32.
To find the total amount of interest John pays on the loan, we can multiply the monthly payment by the total number of payments and subtract the initial loan amount:
Total interest = (P * n) - PV
Total interest = ($144.32 * 48) - $6000
Total interest = $6934.16 - $6000
Total interest = $934.16
Therefore, the total amount of interest John pays on the loan is $934.16.