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Sudnose Ihat & life insurance company insures 5800 40-yeat old den Vunc peop 2 andIne doaln benefitt given year (Aseirte coalh rale 0l 2pol IO0Q people 555,O00_...

Question

Sudnose Ihat & life insurance company insures 5800 40-yeat old den Vunc peop 2 andIne doaln benefitt given year (Aseirte coalh rale 0l 2pol IO0Q people 555,O00_ How much can Lhe company excec Tne cost of Ihie prenlm gamn (or lose) 5100 yeali mswance poMpully can erac Alni (Typo Ahole nurtbt )pront

Sudnose Ihat & life insurance company insures 5800 40-yeat old den Vunc peop 2 andIne doaln benefitt given year (Aseirte coalh rale 0l 2pol IO0Q people 555,O00_ How much can Lhe company excec Tne cost of Ihie prenlm gamn (or lose) 5100 yeali mswance poMpully can erac Alni (Typo Ahole nurtbt ) pront



Answers

Payout on Insurance Policies An insurance company has written 100 policies for $\$ 100,000,500$ policies for $\$ 50,000$ , and 1000 policies for $\$ 10,000$ for people of age $20 .$ If experience shows that the probability that a person will die at age 20 is 0.0012, how much can the company expect to pay out during the year the policies were written?

No that's probably have another life insurance question. Now. We were wanting to find and interpret the expected that. Now. It's important. Remember that expected value is equal to the sum of all the exes times their probabilities. I've got this problem. We're selling a $250,000 1 year term life insurance policy. So 20 year old male for $350. Yeah that means that this company has two different outcomes here. If that person were to pass away Then the company would lose $250,000. But if the man survives the year Then the company makes $350 because that's what his premium is. Now the probability that the male survives is .99 8734. And so the probability that the company makes $350 is .998734. Now that means that the probability that they lose $250,000 is 1 -998734 And that's .001, 266 And so that's the probability that they lose the $250,000. And so computing this would give us are expected value and so we can just type this in just like it looks on a calculator, And this should give us $33 And 50 cents. And so that is the life insurance companies expected value, $33 and 50 cents.

The for this question. You know that for $15.20 we'll get you $1000 of insurance. So we're us. How much money for $75,000 in insurance. So then we can start off by cross. Most pointing to get us 1000 X is equal to $15.20 tooth cents times 75,000. So that will get us 1000 X. Does he call to 1,141,500? And so we divide this by 1000. We will get X is equal to 100 or $1141.5 as the cost for $75,000 of insurance.

For this number we have cost is equal to the score to five A. Plus one where it represents age. We're trying to figure out what would the H. B. If we want the 20 per day. So we're gonna plug in 20 and solve for a. The first thing we have to do is square both sides. To get rid of that roots. That's gonna give us 400 is equal to five A. Plus one Must subtract one on both sides. It's gonna get us 399 is equal to five a. Dividing both sides by five. Gives us the age to be about 79.8 years. Or if you need to run to the nearest whole number that be about 80 years old.

Yeah, that's probably we're dealing with expected value for life insurance company now. The expected value in general is equal to the sum of all the excess times the probability of active. And so it sort of what's going on here. Life Insurance sells a $250,000 1 year term to 20 year old for $200. The probability that the female survives years give my .999544. And we want to compute interpret the expected value For the insurance company. They have to hostilities here 1st, They didn't make $200 And how much they're charging the person. So they end up with a net of $200. And the probability that they make it is given by that .999544. That's because as long as that female survives, they make that money and they don't pay out the life insurance on the flip side of this. The other option is that they lose 250,000. And the probability that that happens is 1 -199544. And so that probability is given by .000456. Again, that's just 1 -2.999544 there, so that if we evaluate this okay, we just had the strangest 1.999544 times 200 plus .0456 times a year of 25 million. 250,000. This should give us $85 And 91 cents. And so what this means is that per client, the firm should expect to meet $85 And 91 cents.


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