By Michael Osborne (auth.)
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Additional info for Multiple Interest Rate Analysis: Theory and Applications
Example text
Time Cash flows Dollars outstanding The number of dollars marked up by (1+r1) 0 1 2 3 p –c1 –c2 –c3 4 –c4 p p(1+r1) – c1 p(1+r1)2 – c1(+r1) – c2 p(1+r1)3 – c1(1+r1)2 – c2(1+r1) – c3 p(1+r1)4 – c1(1+r1)3 – c2(1+r1)2 – c3(1+r1) – c4 The last equation is Eq. 5a) which is equal to zero. p p(1+r1) – c1 p(1+r1)2 – c1(1+r1) – c2 p(1+r1)3 –c1(1+r1)2 – c2(1+r1) – c3 The total number of dollars marked up by (1+r1) is the sum of the cells above, labeled S. Note: The number of times an invested dollar is marked up by (1+r1), and therefore by r1, is S/p.
1057/9781137372772 Four Key Results of Multiple-Interest-Rate Analysis The analysis continues with a numerical example. 5a): {ci for i = 1 to 4} = {3, 1, 4, 2}. 9250. This situation is captured by the following conventional equation and its dual. 9a) applies. 1. 1 contains the values for the four roots (1 + rj) satisfying this equation, and the implied values for the four interest rates (rj). 1 plots the roots and displays the rates. 9a) concerns the meaning of the product in the denominator.
This statement is true no matter which of the n interest rates solving the TVM equation is selected. 1057/9781137372772 Four Key Results of Multiple-Interest-Rate Analysis the unorthodox interest rates enumerates the applications of the orthodox rate (r1) to an invested dollar during amortization. A proof follows. 5a). Col. 2 contains the cash flows. Col. 3 contains the number of dollars outstanding. The elements in Col. 4 contain the number of dollars marked up at each time by (1+r1), and therefore the number marked up by r1.