A sports car is on sale at the local dealership.The price discounted is $12,595 .With 5% down, you can pay $249.34 a month for 60 months to pay for the car which includes interest.What is the total cost of this car if you bought on the installment plan? How much interest would be paid?
after 5% down payment you would owe 11965.25
249.34 times 60 = 14960.40
interest paid = 14960.40 - 11965.25 = $2995.15
(I hope they don't teach you that you can now find the rate of interest to be 2995.15/(11965.15(5)) = .05 or 5% ????)
the actual monthly rate of interest:
let it be i
11965.25 = 249.34( 1 - (1+i)^-60)/i
running it through a good "equation solver" program , I got i = .0076378
the annual rate is .0916 or 9.16%
check:
249.34( 1 - 1.0076378^-60)/.0076378 = 11965.24 , wow, not bad
To calculate the total cost of the car if purchased on the installment plan, we need to consider the down payment, the monthly payments, and the interest.
Let's start by calculating the down payment. The down payment is given as 5% of the total price of the car, which is the discounted price of $12,595. Therefore, the down payment is:
Down payment = 5% of $12,595
Down payment = ($12,595 * 5%) / 100
Down payment = $629.75
Now, let's calculate the total cost of the car. We will add the down payment to the total of all the monthly payments over 60 months. Each monthly payment is $249.34, and since there are 60 months, the total of all the monthly payments is:
Total of monthly payments = $249.34 * 60
Total of monthly payments = $14,960.40
To calculate the total cost of the car, we'll add the down payment to the total of all the monthly payments:
Total cost = Down payment + Total of monthly payments
Total cost = $629.75 + $14,960.40
Total cost = $15,590.15
Therefore, the total cost of the car if purchased on the installment plan is $15,590.15.
Now, let's calculate the amount of interest paid. To find this, we need to subtract the original price of the car from the total cost:
Interest paid = Total cost - Original price
Interest paid = $15,590.15 - $12,595
Interest paid = $2,995.15
Therefore, the amount of interest paid would be $2,995.15.