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This paper provides a new and original formula to calculate the present value of a loan that is paid in different installments. The analysis is extended to various topics, such as calculating the duration of a loan and the value of a swap and develops simplified expressions for both. The simplified expressions developed in this paper may be used in a variety of ways to facilitate and simplify the analysis and calculation of the fair value of a financial instrument. Even though computations may be carried out using software, such as Microsoft Excel, there is much to gain from the new analysis, as it provides insight into the relevant relationships and allows efficient ways of setting up the relevant calculations. |
