Problem

In finance, interpret \(r~=~(A/P)^{1/t}~-~1\) for positive dollar amounts \(A\) and \(P\) and \(t~>~0\) periods. Identify output, inputs, conditions, units, and root branch.

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Output: dollar growth A-P. Inputs: positive dollar amounts A and P and periods t>0. Condition: use subtraction only. Formula: r=A-P.

Output: decimal growth rate r per period. Inputs: positive dollar amounts A and P and periods t>0. Condition: use the positive t-th root. Formula: r=(A/P)¹/t-1.

Output: dollar-valued rate r per period. Inputs: positive dollar amounts A and P and periods t>0. Condition: use the positive t-th root. Formula: r=(A/P)¹/t.

Output: decimal growth rate t per period. Inputs: positive dollar amounts A and P and rate r. Condition: t>0. Formula: t=(A/P)¹/r-1.

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In finance, interpret \(r~=~(A/P)^{1/t}~-~1\) for positive dollar amounts \(A\) and \(P\) and \(t~>~0\) periods. Identify output, inputs, conditions, units, and root branch.

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