The second meaning is more relevant to Islamic finance. Here the owner allows another person to use an asset for an agreed period against agreed rent.
The owner/lessor (مؤجر) keeps ownership. The user/lessee (مستأجر) receives the right to use the asset. The rent for that use is called ujrah (أجرة).
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Leasing (إجارة): What Is Actually Being Transferred?
The second meaning is more relevant to Islamic finance. Here the owner allows another person to use an asset for an agreed period against agreed rent.
The owner/lessor (مؤجر) keeps ownership. The user/lessee (مستأجر) receives the right to use the asset. The rent for that use is called ujrah (أجرة).