A car may be purchased with a $3500 down payment now and 72 monthly payments of $480. If interest rate is 12% compounded monthly, what is the price of the car?

P = 3500 + (480*72) = 38,060.

P = Po(1+r)^n = 38,060,

r = 0.12/12 = 0.01/mo., n = 72 Compounding periods.

Po(1.01)^72 = 38,060, 2.047Po = 38,060, Po = $18,592.16. = Price of car.

The Equation used most often for home and auto loans:

P = Po*r*T/(1-(1+r)^-T)

(Po*0.01*72)/(1-1.01^(-72)) = 38,060, 0.72Po/0.51150 = 38,060,
1.41Po = 38,060, Po = $27,038.67.
= Cost of car.

To find the price of the 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:

Step 1: Convert the annual interest rate to a monthly interest rate.
The annual interest rate is 12%, so the monthly interest rate is 12% divided by 12, which equals 1%.

Step 2: Calculate the present value of the monthly payments using the formula for the present value of an annuity:
PV = C * [1 - (1+r)^(-n)] / r

Where:
PV = Present value of the annuity (in this case, the monthly payments)
C = Amount of each payment ($480)
r = Monthly interest rate (1%)
n = Number of payments (72)

Using these values, we can plug them into the formula:
PV = 480 * [1 - (1 + 0.01)^(-72)] / 0.01

Calculating this will give us the present value of the monthly payments.

Next, let's calculate the present value of the down payment:

The present value of the down payment is simply the amount of the down payment, which is $3500.

Now, let's add the present value of the monthly payments and the present value of the down payment to find the total price of the car:

Total price of the car = Present value of the monthly payments + Present value of the down payment

So, by calculating the present value of the monthly payments and adding it to the present value of the down payment, you will find the price of the car.

Price = 3500 + (480*72) =