Final answer:
The calculation of the total cost paid for the loan, including the down payment, results in $25,000. However, the exact cash price considering the 7.1% interest compounded monthly is not given explicitly, and additional information would be needed to calculate the present value of the car accurately.Therefore, based on the options provided, the cash price of the car is not exact.
Step-by-step explanation:
To determine the cash price of the car that Esther is paying for, we need to calculate the total amount paid for the loan and then add the down payment made at the beginning.
The monthly loan payment is <$355>. The total number of payments over 5 years (5 years x 12 months per year) is 60 payments. To calculate the cash price of the car:
- First, we add up all the monthly payments made: 60 payments x $355 = $21,300.
- Next, we add the initial down payment of $3,700 to the total of the monthly payments: $21,300 + $3,700 = $25,000.
The cash price of the car before the interest from the loan is the sum of the down payment and total payments made for the loan: $25,000. However, since we know that the loan costs 7.1% per year compounded monthly, we must account for this interest in determining the present value of the car.
However, to determine the exact cash price, we would need more information than provided in the scenario to correctly account for the compound interest. Therefore, based on the options provided, the cash price of the car is not exact.