Stupid Bond Question - Prepping for IB Interviews

Was reviewing through technicals in the IB guides from WSO and came across the function to approximate YTM for a bond - been through finance classes and never thought about this.... why does the function take the average of Purchase Price and Face Value to use in the denominator?I would think for the return, you would use the purchase price as the Face Value is already accounted for in the numerator...The formulas below for reference

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