The 2nd comment is on the right track, except he/she is off by one month. Without using Excel spreadsheet and function, here's the back-of-envelope calculation. In my example, the insurance company loans you $184 for 1 month, another $184 for 2 months, and a third $184 for 3 months. If you average out the first and the third installment and make them both $184 for 2 months, you are borrowing total $552 for 2 months. For that 2 months, you interest cost is $16/$552 = 2.9%. Compound it 6 times for an annualized rate, you get (1 + 2.9%) ^ 6 – 1 = 18.7%.

This is a bit tricky to explain, I am not able to get quite to 19% but I can get a good way there.

From your perspective, your effective interest rate is 12.1%. From the companies point of view, their return on investment is >15%. You can get 12.1% using relatively straightforward logic. TFB's point (an apparent 2% cost is really something substantially more) has been very well made. Unless you have a foolproof way to invest your money at a yield of 12.1%, pay it up front if you can.

The way I thought about it is this: how much is the insurance company loaning you and when?

In the case where you pay the company everything up front, they are loaning you no money for no time.

According to TFB's table: With the installment plan, you pay 188 at the beginning (the company is owed 552 – remember 4 of that is charge), then 2 months later pay another 188 (the company is owed 368), then one month later you pay another 188 (the company is owed 184), in another month you pay 188 again at which point the company is owed nothing.

You can think of it this way: You borrow:

you borrow 184 for 4 months.
you borrow an additional 184 for 3 months.
you borrow a last 184 for 2 months.

The maximum YOU borrowed is 552. The cost of these loans must be $16 which is about 12.1%.

Here is where it gets tricky TFB's notes that the insurance company's net outlay is only 548 (they got your $4 charge at the beginning so are only 548 out of pocket NOT 552). Therefore, from their perspective:

172 for 4 months.
188 for 3 months.
188 for 2 months.

At the end of this 4 month period they are $16 ahead. This gives them a return of 12.4%.

If you consider the fact that they do this twice and the second time around they are only $532 out of pocket (having received the $16 from you) AND they have a different repayment schedule (this one take place over 3 months not 4!) this gets to almost 15.4% annual return.

I can't quite get to the 19%, but I suspect it is computed correctly and probably takes into account the exact dates of booking the payments and that this is only 7 out of 12 months.

The big point here is that the 2% is incorrect since even in the first instance this represents 4 months. The annual yield for the insurance company even if they let you put off paying anything to the end of the 4 month period is over 6%.

Where does that 19% come from?