Lupe made a down payment of $2000 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 11% per year compounded monthly. Under

A) The cash price of the car can be found using the formula for present value of an annuity: PV = PMT * [(1 - (1+r)^-n) / r] Where PV is the present value (cash price) of the car, PMT is the monthly payment of $230, r is the monthly interest rate (11% / 12 = 0.917%), and n is the number of months in the loan term (36). Plugging in these values, we get: PV = $230 * [(1 - (1+0.00917)^-36) / 0.00917] PV = $7,386.34 Adding the down payment of $2,000, the total cash price of the car is: Cash price = $7,386.34 + $2,000 = $9,386.34 Therefore, the cash price of the car is $9,386.34 (rounded to the nearest cent). B) The total amount of interest paid for the purchase can be found by subtracting the cash price of the car from the total amount paid over the 36-month loan term. The total amount paid is simply the sum of all monthly payments: Total amount paid = $230 * 36 = $8,280 Subtracting the cash price of $9,386.34 from the total amount paid, we get: Interest paid = $8,280 - $9,386.34 = -$1,106.34 This negative value means that Lupe actually paid less than the cash price of the car because the interest rate was compounded monthly, resulting in a lower total amount of interest paid. Therefore, the interest paid for this purchase is -$1,106.34 (rounded to the nearest cent).