Why Is the Interest Rate a More Significant Factor in the Early Exercise of an American Put than a Call?

The interest rate is more significant for an American put because exercising it yields immediate cash (the strike price) which can be invested to earn interest. Higher interest rates increase the value of this immediate investment, thus increasing the incentive for early exercise.

For a call, high interest rates increase the cost of capital to acquire the asset, reducing the incentive for early exercise.