Easy Books is a fully functional double-entry accounting application. The app is developed by Geode Software and is available as a free download. It comes with space for 120 entries (transactions) and some example companies for you to try it out. You can upgrade with a one-off purchase within the app, and you decide what features you want, so you only pay for what you need.
Easy Books is ideally suited to small businesses and 'one-man bands'. We have had lots of feedback from people who love the iOS version of this app; builders, contractors, consultants, musicians, farmers, treasurers, and, of course, bookkeepers. Together they have sent suggestions (via the feedback form) which have improved the app over time.
Note: While the software is classified as free, it offers in-App Purchases.