SOLUTION: A car was purchased for $1500 down and payments of $265 at the end of each month for four years. Interest is 9% compounded quarterly. (a) What was the purchase price of the car?�

Question 1207424: A car was purchased for $1500 down and payments of $265 at the end of each month for four years. Interest is 9% compounded quarterly. (a) What was the purchase price of the car? (b) How much interest will be paid?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
payments at the end of each month = 265.
number of payments = 4 * 12 = 48.

interest rate is 9% compounded quarterly.
the quarterly interest rate is 9/4 = 2.25% per quarter..
the quarterly growth factor is 1.0225.
the effective annual growth factor is 1.0225 ^ 4 = 1.0983083319.
the effective monthly growth factor is 1.0983083319 ^ (1/12) = 1.007444443.
the effective monthly growth rate is that minus 1, then multiplied by 100 = .7444443%.

i used the texas instruments business analyst 2 calculator to solve this.
inputs are:
present value = 0
payments at the end of each month are -265.
future value = 0
interest rate per month = .7444443%.
number of payments = 48.

calculator says that the present value of the loan payments is equal to 10,662.52591
round to the nearest penny to get 10662.53
add the 1500 down payment to that to get 12,162.53
that's the price of the car.
round as required.

the online calculator at works the same was as the texas instrument calculator, except that it rounds the results to the nearest penny.

the results from using that calculator are:

the amount of interest that was paid was the sum of all the payments minus the present value of the loan = 48 * 265 minus 10,662.53 = 2057.47.

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SOLUTION: A car was purchased for $1500 down and payments of $265 at the end of each month for four years. Interest is 9% compounded quarterly. (a) What was the purchase price of the car?�

SOLUTION: A car was purchased for $1500 down and payments of $265 at the end of each month for four years. Interest is 9% compounded quarterly. (a) What was the purchase price of the car?�