"I'm calling for a couple of reasons.."
Good Morning/Afternoon/Evening! My name is <name> calling on behalf of <Insurance Company Name>. Am I talking to <customer name>?
Mr/Ms <customer name>. Actually, I'm calling for a couple of reasons. The first is to make sure that you and your family are presently covered with regard to investments and security. You are, I assume, aren't you?
Prospect: Yes, we are fully covered.
That's good news. The second reason for calling is that my company is currently offering some products specifically designed to improve your situation in that regard.
Would this be a good time to talk to you for a few moments regarding these improvements--or can we set aside a more convenient time?
NOTE: I've been asked why the word "actually" is inserted. The answer is that it's conversational. It's a finesse that promotes dialogue rather than monologue. Anything that will foster conversation will help you with a prospect.
So now you have three questions in your script rather than two. They address: 1) Talking to right person. 2) Current situation 3) Good time to talk.
Finally, in your experience the prospects are using Current Situation as a tool to dismiss you. (Already has insurance). With the new script you are using the Current Situation as something to build on.