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## More on expected value

# Term life insurance and death probability

## Video transcript

I'm thinking about getting
life insurance because I have a mortgage and
I have a young son and another baby on the way. And so if anything
were to happen to me, I'd want them to at least be
able to pay off the mortgage and then maybe have some
money left over for college and to live, and whatever else. And so I went to the
insurance company, and I said I want to
get a $1 million policy. And what I'm actually
getting a quote on is a term life policy,
which is really-- I just care about
the next 20 years. After those 20 years, hopefully,
I can pay off my mortgage. There'll be money saved up. Hopefully, my kids
would kind of at least have maybe gotten
to college or I would have saved up
enough money for college. So that's why I'm willing
to do a term life policy. The other option is to do
a whole life policy, where you could pay a
certain amount per year for the rest of your life. At any point you die, you
get the million dollars. In a term life, I'm only
going to pay a $500 per year for the next 20 years. If at any point over
those 20 years I die, my family gets a million. At the 21st year, I have
to get a new policy. And since I'm going
to be older and I'd have a higher chance
of dying at that point, then it's probably going
to be more expensive for me to get insurance. But I really am just worried
about the next 20 years. But what I want to
do in this video is think about given
these numbers that have been quoted to me by
the insurance company, what do they think that
my odds of dying are over the next 20 years? So what I want to think
about is the probability of Sal's death in
20 years, based on what the people at
the insurance company are telling me. Or at least, what's
the maximum probability of my death in order
for them to make money? And the way to think about it,
or one way to think about it, kind of a
back-of-the-envelope way, is to think about what's the
total premiums they're getting over the life of this
policy divided by how much they're insuring me for. So they're getting $500
times 20 years is equal to, that's $10,000 over the
life of this policy. And they are insuring
me for $1 million. So they're getting-- let's
see those 0s cancel out, this 0 cancels out--
they're getting, over the life of the
policy, $1 in premiums for every $100 in insurance. Or another way to
think about it. Let's say that there were 100
Sals, 100 34-year-olds looking to get 20-year term
life insurance. And they insured all of them. So if you multiplied
this times 100, they would get $100 in premiums. This is the case where
you have 100 Sals, or 100 people who are
pretty similar to me. 100 Sals. They would get $100 in premium. And the only way that they
could make money is if, at most, one of those Sals-- or really
just break even-- if, at most, 1 of those Sals were to die. So break even if
only 1 Sal dies. I don't like talking about this. It's a little bit morbid. So one way to think
about it, they're getting $1 premium
for $100 insurance. Or if they had 100 Sals, they
would get $100 in premium, and the only way they
would break even, if only 1 of those Sal dies. So what they're really
saying is that the only way they can break even is if
the probability of Sal dying in the next 20 years is less
than or equal to 1 in 100. And this is an
insurance company. They're trying to make money. So they're probably
giving these numbers because they think the
probability of me dying is a good-- maybe it's 1
in 200 or it's 1 in 300. Something lower, so
that they can insure-- one way to think about it--
they could insure more Sals for every $100 in premium
they have to pay out. But either way, it's a
back-of-the-envelope way of thinking about it. And it actually makes me
feel a little bit better because 1 in 100 over the
next 20 years isn't too bad.