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[Solved] Replicating a cash flow with single-period loans. We refer to the example described on page 93 of the textbook. Let c be any n -vector representing

Question: Replicating a cash flow with single-period loans. We refer to the example described on page 93 of the textbook. Let \(c\) be any \(n\) -vector representing a cash flow over \(n\) periods. Find the coefficients \(\alpha_{1}, \ldots, \alpha_{n}\) of \(c\) in its expansion in the basis \(e_{1}, l_{1}, \ldots, l_{n-1}\), i.e.,

\[c=\alpha_{1} e_{1}+\alpha_{2} l_{1}+\cdots+\alpha_{n} l_{n-1}\]

Verify that \(\alpha_{1}\) is the net present value (NPV) of the cash flow \(c\), defined on page 22 of the textbook, with interest rate \(r\).

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