When you purchase an application from the iOS App Store, it is saved in your App Store account. So you can always reinstall it on your device, or install it on a new device, without having to buy it again.
Note: The version of the screenshots below may differ from yours, but the content of the article applies to your version as well.
To reinstall the app, open the iOS App Store and go to your account:
Once in your account, go to "Purchased":
Next, locate the application to be reinstalled and click on the installation icon:
Please note: This procedure is only applicable if you have purchased the App you wish to reinstall with the account currently active on your iOS device.