$7.$ An engineering student bought a car at a local used car lot. Including tax and insurance, the total price was $300000.$ He is to pay for the car in $12$ equal monthly payments, beginning with the first payment immediately $($in other words, the first payment was the down payment$).$ Nominal interest on the loan is $12\%,$ compounded monthly. After six payments $($the down payment plus five additional payments$),$ he decides to sell the car. A buyer agreed to pay a cash amount to pay off the loan in full at the time the next payment is due and also to pay the engineering student $100000.$ If there are no penalty charges for this early payment of the loan, how much will the car costs to the new buyer?