Your house is worth 500k. Every year, there is a 0.02% chance that a fire will occur and cause a complete damage. In addition, there is a 0.05%...

The insurance premium will be equal to the expected loss, plus the profit margin for the insurance company.The expected loss is the probability of the loss times the magnitude of the loss, added up for all possible outcomes: 0.02*500,000 + 0.05*200,000 = 10,000 + 10,000 = 20,000Adding a 20% profit margin for the insurance company means we multiply this by 1.20:20,000*1.20 = 24,000The annual insurance premium is therefore $24,000.By "risk...

The insurance premium will be equal to the expected loss, plus the profit margin for the insurance company.

The expected loss is the probability of the loss times the magnitude of the loss, added up for all possible outcomes:

0.02*500,000 + 0.05*200,000 = 10,000 + 10,000 = 20,000

Adding a 20% profit margin for the insurance company means we multiply this by 1.20:

20,000*1.20 = 24,000

The annual insurance premium is therefore $24,000.

By "risk aversion parameter", I'm assuming you mean relative risk aversion parameter, which for y = 1 means that your utility function is logarithmic:

U = ln(C)

(As a reminder, normally it would be U = 1/(1-y) * (C^(1-y) - 1), but for y = 1 there is a special limit case which is U = ln(C).)

Ignoring all other spending, your consumption will be:

$76,000 if you buy insurance
$100,000 if you don't buy insurance and nothing happens (93% probability)
-$100,000 if you don't buy insurance and you get a small fire (5% probability)
-$400,000 if you don't buy insurance and you get a large fire (2% probability)

We can immediately see that you must buy the insurance, because your consumption goes negative and therefore your utility goes to negative infinity if you don't buy the insurance and you have a fire. You simply cannot afford to have a fire.

Under these conditions, your reservation price is actually $100,000. You are willing to spend all of your money to insure your house, because you cannot afford what would happen if you didn't.

In "A Separate Peace" by John Knowles, how do Finny and Gene complete each other?

Gene and Finny complete each other in the same way that the two halves of a Yin and Yang make a complete circle.  Gene and Finny may be best friends, but they are very different in a lot of ways.  Finny embodies a carpe diem attitude, while Gene is much more cautious and reserved.  Those two personalities are constantly playing off of each other, and they serve to balance each boy out.  Without Gene, Finny...

Gene and Finny complete each other in the same way that the two halves of a Yin and Yang make a complete circle.  Gene and Finny may be best friends, but they are very different in a lot of ways.  Finny embodies a carpe diem attitude, while Gene is much more cautious and reserved.  Those two personalities are constantly playing off of each other, and they serve to balance each boy out.  Without Gene, Finny would not ever consider the consequences of his actions (kind of like how Jiminy Cricket completes Pinocchio).  Without Finny, Gene would never leave the confines of his dorm to stop studying.  It's almost like John Knowles took a regular person's warring impulses between doing what a person should do and doing what a person might want to do and created two caricatures of those personality types.   One caricature is Gene, and the other is Finny.  Put together, they mirror a more realistic, complete person.  

Why did John baptize (MK 1)? What did his baptism accomplish? What are the limits of his baptism?

According to Mark Chapter 1, John the Baptist fulfilled the role of the "messenger," a person who, according to prophesy, would be sent before the Son of God (Jesus), to "prepare the way." "Preparing the way" means to make people ready to accept the Gospel that Jesus would preach, and to prepare people's hearts and minds to follow Christ without reserve. We can think of John the Baptist as the first person who proselytized or...

According to Mark Chapter 1, John the Baptist fulfilled the role of the "messenger," a person who, according to prophesy, would be sent before the Son of God (Jesus), to "prepare the way." "Preparing the way" means to make people ready to accept the Gospel that Jesus would preach, and to prepare people's hearts and minds to follow Christ without reserve. We can think of John the Baptist as the first person who proselytized or "converted" people into the Christian faith, although this conversion occurred prior to folks' interacting with Jesus himself. 

John's baptism resulted in an individual being forgiven of all their sins. The limit of his baptism was that it did not invite the Holy Spirit to reside within that individual. John said that though he himself baptized with water, Jesus (the man who would come after him) would baptize believers in the Holy Spirit. Once the Holy Spirit was invited to inhabit a person's soul, that person would no longer be susceptible to sin. Thus, Jesus' baptism would not only forgive a person all their sins, but would also protect them from future sin and help keep their souls pure from that moment forward. 

Alice promises to pay Bob $1000 today, $2000 in one year, $3000 in two years, and so on indefinitely. Assume that the interest rate is 2%,...

Alice promises to pay Bob $1000 today, $2000 in one year, $3000 in two years, and so on indefinitely. The interest rate to be used is 2%, compounded continuously.

The amount given by Alice to Bob at the beginning of year n is given by (n+1)*1000.

As interest is compounded continuously and the amount is received at the beginning of the year, the present value of an amount received after n years is A =...

Alice promises to pay Bob $1000 today, $2000 in one year, $3000 in two years, and so on indefinitely. The interest rate to be used is 2%, compounded continuously.

The amount given by Alice to Bob at the beginning of year n is given by (n+1)*1000.

As interest is compounded continuously and the amount is received at the beginning of the year, the present value of an amount received after n years is A = (n+1)*1000/e^(0.02*n)

The total present value of Alice's promise is

`1000+ sum_(n=1)^(oo)(n+1)*1000/e^(0.02*n) `

= 2.54942*10^6

Alice would make the largest payment to Bob approximately at the start of year 49.

How does Charles Dickens represent the Cratchit family as being poor?

Your question refers to the family of Ebeneezer Scrooge's employee, Bob Cratchit. While Scrooge is known for his extreme thriftiness, dark temper, and lack of charity during the "present" setting of the story, Cratchit's goodwill in spite of financial poverty is presented in sharp contrast to that characterization. We learn of the poorness of Cratchit and his family through both Scrooge's comments about them and the omniscient narrator's description of their appearance and home life.

...

Your question refers to the family of Ebeneezer Scrooge's employee, Bob Cratchit. While Scrooge is known for his extreme thriftiness, dark temper, and lack of charity during the "present" setting of the story, Cratchit's goodwill in spite of financial poverty is presented in sharp contrast to that characterization. We learn of the poorness of Cratchit and his family through both Scrooge's comments about them and the omniscient narrator's description of their appearance and home life.

Our first notice of Cratchit is in chapter one. In this scene he is busy in the background with his clerical work when Scrooge's nephew visits their office to invite Scrooge to dinner. Grumbling to himself after Nephew Fred leaves, Scrooge compares Fred and Cratchit to one another as people who ought to be too poor to be so happy at Christmas time.

In chapter three when the Ghost of Christmas Present takes Scrooge to observe the Cratchit family, the narrator implies that Scrooge is incredulous that the Ghost would bother to bless this family even though Bob only earns "fifteen bob a-week"; for present-day Scrooge, a person's worth is defined by economic status. The Cratchits are here described as bravely making the best of what little they have. Mrs. Cratchit, for example, is "dressed out but poorly in a twice-turned gown, but brave in ribbons, which are cheap and make a goodly show for sixpence". Their daughter Belinda is also "brave in ribbons", and their son Peter wears a too-large shirt with collars that he has borrowed from his father for this special occasion of Christmas dinner. Cratchit arrives home in this scene in his "threadbare" clothes that someone has attempted to darn and brush to make him look seasonable. The narrator also comments about the fact that Cratchit's sleeve cuffs are not capable of being made more shabby. The older Cratchit children talk of apprenticeships that will help add to the family's income, Martha already an apprentice at a milliner's shop and Peter on the verge of finding work soon. We are told that they are "not a handsome family", "not well dressed", "their shoes were far from being water-proof" and they have scanty clothing. When their dinner goose is served, the whole family is merry about it because such a dish is a rarity in their household.

Dickens balances these bits of imagery with reassurance that in spite of their poverty, the Cratchit family members are unfailingly grateful for one another's company and devotion. Their poorness is after all only financial, because they are wealthy in human kindness. The juxtaposition of the family's poverty and bravery in the face of all its hardships are a shocking thing for Scrooge to see, and this is part of the catalyst for Scrooge's decision to reform himself.

The story is mostly about how two kidnappers did what?

"The Ransom of Red Chief" is an early example of what in Hollywood is called a "Busted Caper" story. A criminal, or two partners, or a whole group of criminals plan to commit a crime and something goes wrong which results to their downfall. In O. Henry's story, the kidnappers, Sam and Bill, are making the mistake of moving into a type of crime with which they have no previous experience. They are obviously con artists. They want the ransom money in order to perpetrate another of the kind of swindles with which they are familiar. But in order to get the money to work the "fraudulent town-lot scheme," they have to execute another crime successfully. They may think their biggest problem as kidnappers will be in dealing with the boy's father, but it turns out that the real problem is dealing with the boy himself.

The story is treated comically. Red Chief turns out to be more than they can handle. He loves being kidnapped and loves playing Indian, sleeping on the ground, cooking over an open fire, and never having to go to school. There are several reasons why Sam and Bill can't handle their victim, even though he is only ten years old. One reason is simply that they have had no experience in dealing with children, especially with rambunctious small boys. Another reason is that they can't use physical force. If they were violent with Red Chief they would make him a dangerous enemy. Once they returned him to his father he would be able to identify his kidnappers and tell a lot about them. In many cases of kidnapping children, the victim is murdered to prevent the child from giving information about the criminals and also to prevent the child from testifying against them when they get caught. Sam and Bill obviously are not killers. But if they returned the boy to his father with bruises and abrasions they would make dangerous enemies of both Red Chief and his father. Furthermore, once they become kidnappers they lose any moral authority they might possess as adults--and Red Chief knows it! How can they ask him to behave when they are misbehaving so flagrantly themselves? 

'You know, Sam,' says Bill, 'I've stood by you without batting an eye in earthquakes, fire and flood--in poker games, dynamite outrages, police raids, train robberies and cyclones. I never lost my nerve yet till we kidnapped that two-legged skyrocket of a kid. He's got me going. You won't leave me long with him, will you, Sam?'

In a busted-caper story things go from bad to worse, and the criminals can't just walk away from the mess they have made. What seems like a simple crime turns into a very complicated one. An excellent example of a busted-caper movie is Fargo (1996), starring William H. Macy as Jerry Lundegaard, who hires two freakish characters to kidnap his wife. In the end the wife is dead, her father, who was supposed to pay a million dollars ransom, has been shot dead, one of the kidnappers has murdered the other, an innocent park-lot attendant has been killed, and Jerry Lundegaard is captured and will undoubtedly get a death sentence. Like Sam and Bill in the O. Henry story, the problem is inexperience and incompetence.

Sam and Bill use a lot of big words and malapropisms in their dialogue, but they are really ignorant men and not overly bright. If they were intelligent they wouldn't be down to their last six hundred dollars at their time of life. They find it is easy to kidnap Red Chief and easy to keep him a hostage, but it is hard to get rid of him. The father refuses to pay the fifteen-hundred dollars they demand and offers to take the hellcat off their hands if they pay him two hundred and fifty dollars. They have to trick the kid in order to get him to go home.

As the story opens, the narrator is in jail, awaiting his execution on the following day. Find and write two of the lines from the story that show...

Poe never explicitly says if the narrator is in prison. Instead, the narrator says, at the beginning of the story, that he writes because “to-morrow I die, and to-day I would unburthen my soul.” The assumption is that the narrator is a condemned prisoner. There is another indication that he may be in prison at the end of the story, when the narrator says that the cat, in making the existence of the murder known...

Poe never explicitly says if the narrator is in prison. Instead, the narrator says, at the beginning of the story, that he writes because “to-morrow I die, and to-day I would unburthen my soul.” The assumption is that the narrator is a condemned prisoner. There is another indication that he may be in prison at the end of the story, when the narrator says that the cat, in making the existence of the murder known to the police, had “consigned me to the hangman.” It’s pretty clear that he’s been caught.

Another question (maybe a better one) about the frame is, why bother? In other words, why does Poe choose to tell this story in this way, as the written confession of a man who has already been found guilty of a horrible crime and who is about to be executed? Especially since the framing fiction gets such scant attention we have to guess from just a few words what the present state of the narrator is. The answer I think lies in Poe’s desire to create the maximum emotional effect, in this case horror and dread. The frame provides a context within which the story can be conveyed to the reader (the fictive written confession), but also changes the way the reader encounters those events—rather than using a third person narrator to “show” the reader what happens, everything we know comes from the point of view of a homicidal maniac. The events he relates are horrifying, but perhaps even more horrifying is his madness.