Financial Modeling in Practice by Michael Rees

Author:Michael Rees
Language: eng
Format: epub
ISBN: 9781118904008
Publisher: Wiley
Published: 2018-04-16T00:00:00+00:00

This gives:

The backward pass then calculates C2 from C3 (to give ), and then C1 from C3 and C2 (to give ), so that:

On the other hand, instead of explicitly solving the equations in this way, one could use matrix algebra to express the last three equations (since the first equation has solution ) as:

Therefore, the vector of Ci can be found by matrix inversion:

This can be readily calculated in Excel using the MINVERSE function.

The file Ch18.5.MINV.SumofPowers.xlsx shows these calculations, as well as the coefficients that result for the first, second, third, fourth and fifth powers. Note that the results are formatted using Excel's Fraction formatting option; Figure 18.6 shows a screen-clip.

FIGURE 18.6 Calculation of Sums of the Powers of Integers Using MINVERSE

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