Now we will apply this tool to the task of finding out the monthly amount of a loan payment. Suppose someone borrows P to purchase a new car. The bank issuing the automobile loan charges interest at the annual rate of r compounded n times per year. The length of the loan will be t years. The monthly payment can be calculated if we apply the principle that the present value of all the payments made must equal the amount borrowed. Suppose the payment amount is the constant x. If the first payment must be made at the end of the first compounding period, then the present value of all the payments is