7 Suppose we are borrowing $1,000 at 12% annual interest with 60 monthly payments. Assume equal payments are made at the end of month 1, month 2, . . . month 60. We know that entering into Excel the function

 PMT(.01, 60, 1,000)

would yield the monthly payment ($22.24).

It is instructive to use LP to determine the montly payment.

Let p be the (unknown) monthly payment. Each month we owe .01  (our current unpaid balance) in interest. The remainder of our monthly payment is used to reduce the unpaid balance. For example, suppose we paid $30 each month.

At the beginning of month 1, our unpaid balance is $1,000.

Of our month 1 payment, $10 goes to interest and $20 to paying off the unpaid balance. Then we would begin month 2 with an unpaid balance of $980. The trick is to use LP to determine the monthly payment that will pay off the loan at the end of month 60.