An installment loan is an arrangement between a lender of money and a borrower in which the lender gives the borrower a fixed sum of money called the loan principal which he expects will be repaid in a specified number of equal periodic payments. The process of repaying a loan in installments is called amortization. As in most loan agreements, the borrower pays a fixed rate of interest on the outstanding balance of the unpaid principal. Each fixed periodic payment is the sum of two parts: the interest payment calculated as described and the principal payment equal to the difference between the fixed total payment and the interest payment. Thus part of each payment goes toward paying off the total interest and part toward paying off the loan itself. The sum of all interest payments is called the finance charge; the sum of all principal payments is the loan principal. Example 1. A $1,000 loan is to be repaid in 12 monthly installments of equal size. The interest rate is 18% per year or 1.5% per month. From standard amortization tables (Ref. 5) or by algebraic formula (shortly to be derived) the required fixed monthly payment is $91.68. Table 1 is a table of payments and balances by month as the loan progrssses. It was necessary to reduce the final payment to $0.02 in order to force the final balance to be zero. The adjustment is necessitated by rounding errors. The loan principal, number of payments, and interest rate are the loan assumptions from which the fixed monthly payment, finance charge, and all other variables are derived.