For insurance, why should you refuse $4,000/year for only 10 years and prefer $500/year indefinitely?

Question

_{Source: p 336, Personal Finance For Canadians For Dummies (4 ed, 2006; but a 5 ed (2010) exists) by T. Martin, E. Tyson}

“Cash value policies are all paid up after x years. You don’t want to be paying life insurance premiums for the rest of your life, do you?”

[...] Imagine that [1.] you’re currently paying $500 a year for auto insurance, and
[2.] an insurance company comes along and offers you a policy for $4,000 per year. The representative tells you that after 10 years, you can stop paying and still keep your same coverage.
[3.] We’re sure that you wouldn’t fall for this sales tactic, but many people do when they buy cash value life insurance.

I generalise the quote above to all insurance, and not only 'auto insurance'. Why is 3 deceptive and harmful? The use of We’re sure suggests something obvious which I have neglected.

I assume that one needs insurance for some good or service for at least 30 years. Then 2 (a total of $4,000 x 10 years) appears cheaper than ($500 x ? years), because the breakeven number of years is $4000*10/$500 = 80 years.

Answer 1

The breakeven amount isn't at 8 years. You calculated how many years of paying $500 it would take to break even with one year of paying $4000. 8 x 10 years = 80 years. So by paying $500/year it will take you 80 years to have spent the same amount ($40000 total) as you did in 10 years.

At this point it may seem obvious what the better choice is.

Consider where you'll be after 10 years:

In scenario #1 you've spent $5000 ($500*10) and have to continue spending $500/year indefinitely.

In scenario #2 you've spent $40000 ($4000*10) and don't have to pay any more, but you currently have $35000 ($40000 - $5000) less than you did in scenario #1.

If you had stayed with scenario #1 you could invest that $35000 at a measly 1.43% annual return and cover the $500 payments indefinitely without ever dipping into your remaining $35000. Most likely over the long term you'll do better than 1.43% per year and come out far ahead.