Which cloud computing service model will enable an application developer to develop, manage, and test their applications without the expense of purchasing equipment?

Platform as a Service (PaaS)

Explanation:

There are three broad cloud computing service model:

Infrastructure-as-a-Service (IaaS) is a cloud-computing service model in which a vendor provides users access to computing resources such as servers, storage and networking.

Platform as a service (PaaS) is a cloud-computing service model that provides users (mostly application developer) with a cloud environment in which they can develop, manage and deliver applications. This is the required cloud computing service model for the case in question.

Software as a service (SaaS)  is a cloud-computing service model that provides users with access to a vendor’s cloud-based software. Users do not install applications on their local devices. Instead, the applications reside on a remote cloud network accessed through the web or an API.