Jane agrees to buy a car for a down payment of $4000 and payments of $260 per month for 9 years. If the interest rate is 9% per year, compounded monthly, what is the actual purchase price of her car? (Round your answer to the nearest cent.)

i = .09/12 = .0075

n =9(12) = 108

cash value of car
= 4000 + 260(1 - 1.0075^-108)/.0075
= ...

To find the actual purchase price of Jane's car, we need to calculate the present value of the monthly payments and the down payment.

First, let's calculate the present value of the monthly payments using the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

where:
PV = Present value
PMT = Payment per period
r = Interest rate per period
n = Number of periods

In this case, Jane will make monthly payments over 9 years, so n = 9 * 12 = 108 months.
The payment per month is $260, and the interest rate per month is 9% / 12 = 0.75%.

Plugging these values into the formula, we get:

PV = $260 * [(1 - (1 + 0.0075)^(-108)) / 0.0075]

Now, let's calculate the present value of the down payment. Since it is a one-time payment, its present value is simply $4000.

Finally, we can calculate the actual purchase price by adding the present values of the monthly payments and the down payment:

Actual Purchase Price = Present Value of Monthly Payments + Present Value of Down Payment

Actual Purchase Price = PV + $4000

Now, let's calculate the actual purchase price.