ABSTRACT
A loan is defined as a single payment from one person to another. In return the recipient agrees to repay the loan in an agreed upon way based on an agreed upon interest rate. The fundamental idea is simple: the present value (computed using the agreed upon interest rate) of the repayments must be equal to the present value of the loan at the time the loan made. In the most common scenario the recipient agrees to make a sequence of level payments each period. Each payment must pay off the interest due at that time and reduce the amount still due on the loan. This chapter discusses the problem of computing the required payment based on the interest rate and payment frequency. In addition the problems of computing the loan balance and interest due at any time are considered. The construction of an amortization table which computes the loan balance as well as the interest and principal reduction portion of each payment is discussed. Amortization tables which use the TI BA II Plus AMORT worksheet as well as Microsoft Excel are considered. Scenarios in which the payments are not constant are also considered. An alternative strategy in which only the interest due is paid at the end of each period (sinking funds) is considered. Finally, the question of computing the effective annual rate of interest based on the loan amount, payments, and number of payments is considered.
