Exam 8: Contingent Payments

An individual age 50 is promised a payment of $8,000 if he is alive at age 55.If he dies within the next 5 years,his estate will get ½ of this amount,payable at the time that he would have turned 55.You are given the probability of a 50 year old surviving to age 55 is 0.9464.If the interest rate is i = 5%,how much will it cost this individual to buy this payment scheme?

When John and Carl play a game,John wins,on average,2 out of every 5 games played.Today they agree to play until John wins one game or until three games have been played,whichever comes first.What is the probability that John wins one game today?

While driving from his house to work each day,Jack Hammer passes 3 stoplights.If the probability of getting a red light is 1/3 for each of the 3 lights,what is the probability that Jack hits at least one red light?

Students who take drivers education have a 2% probability of having an accident in their first year of driving,while students who do not take drivers education have a 10% probability.Statistics show that the average cost of an accident is $8500.Statistics also show that 70% of new drivers have taken drivers education.What is the expected cost of an accident per driver in their first year of driving?

Recent statistics show that the stock market (as measured by the TSE index)goes up in a day about 60% of the time and goes down the other 40% of the time.Statistics also show that if the market goes up one day,then it goes up the next day 70% of the time and down 30% of the time.But if the market goes down one day,then it goes up the next day 80% of the time and down 20% of the time.What is the probability that in three consecutive days,the market goes up for two of the days and down for one of the days?

A 6-sided die has been weighted so that 5 or 6 comes up 3 times as often as 1 or 2.Also,3 or 4 comes up 2 times as often as 1 or 2.Player A wins $6 if 1 comes up,$5 if 2 comes up and $4 if 3 comes up.Player B wins $3 if 4 comes up,$2 if 5 comes up and $1 if 6 comes up.What is the value of E[A] - E[B],where E[A] is the expectation of winning for player A and E[B] is the expectation of winning for player B?

A large hat contains five $10 bills,seven $5 bills and ten $1 bills.In a game,you are allowed to reach in and pull two bills at random from the hat.If both bills are of the same denomination,you get to keep both of them.In order to make this a fair game,how much should you pay to participate in this game?

A 10-year $5000 par value bond pays interest at j₂ = 7%.The probability that a payment is defaulted,given that all previous payments were made,is 3%.What is the purchase price to yield j₂ = 6%.

For a $1 ticket,a lottery offers the following prizes: •1 prize of $50,000 •10 prizes of $10,000 •100 prizes of $100 •4000 prizes of 5 free ticket If 250,000 tickets are sold,what is the expectation per ticket?

A student has 3 exams.The probability that he does "well" on his first exam is 80%.However,his performance on the remaining two exams depends on how "well" he did on the previous exam.The probability of doing "well" on an exam is 95% if the previous exam was done "well",but only 50% if the previous was not done "well".What is the probability he does "well" on exactly 2 of his 3 exams?

For an investment of $20,000 today at j₂ = 4%,you expect to receive three payments of $R,one each at the end of 1,2 and 3 years.If the probability of default for any payment is 3%,what should the value of R be?

A 6-sided die has been weighted so that 5 or 6 comes up 3 times as often as 1 or 2.Also,3 or 4 comes up 2 times as often as 1 or 2.Player A wins $6 if 1 comes up,$5 if 2 comes up and $4 if 3 comes up.Player B wins $3 if 4 comes up,$2 if 5 comes up and $1 if 6 comes up.Player B wins $3 if a 4 comes up,$2 if a 5 comes up and $1 if a 6 comes up.What is player B's expected winnings?

A perishable product is purchased by a retailer for $5 and is sold for $7.If an item is not sold during the day,the retailer loses $5.Past history has shown that there is a 30% chance of selling 28 of these products in a day,a 28% chance of selling 29 of them in a day,a 25% chance of selling 30 of them in a day and a 17% chance of selling 31 of them in a day.If you order 30 of the items per day,what is your expected daily profit?

A person,who is currently age 50,invests $A today.She is to receive two payments of $5000,one when she reaches age 55 and the second when she reaches age 60.The first payment is guaranteed,but the second payment is paid only if she is alive at age 60 to collect it.You are given the probability of a 50 year old female surviving to age 55 is 0.9867 and surviving to age 60 is 0.9654.If the interest rate is 4%,what is the value of A?

Students who take drivers education have a 3% probability of having an accident in their first year of driving,while students who do not take drivers education have a 9% probability.Statistics show that the average cost of an accident is $7000.Statistics also show that x% of new drivers have taken drivers education.If the expected cost of an accident per driver in their first year of driving is $394.80,what is the value of x?

A $5000 bond pays interest at j₂ = 4% and is redeemable at par in 5 years.The desired yield is j₂ = 5%.What price should you pay for this bond if the probability of any payment being defaulted is 1%,given that all previous payments were paid?

The ABC company lends $A to a person who agrees to pay back $500 at the end of every three months for two years.ABC estimates there is a 2% chance this person will default on a payment.If the interest rate on the loan is j₄ = 6%,what should be the value of A?

A fair standard die is rolled until a six appears.If X is the number of rolls that are necessary.What is the probability that X ≤ 2?

A 10-year $5000 par value bond pays interest at j₂ = 7%.The probability of default in any 6-month period is 3%.What is the purchase price to yield j₂ = 6%.

On the day his child turned age 1,Sam bought a scholarship plan that pays $8000 on the day his child turns 18 but only if his child attends university.The probability of a 1-year old attending university at age 18 is 55%,while the probability of a 1-year old surviving to age 18 is 0.989.If j₁ = 4%,what is a fair price to pay for this scholarship plan (ignoring expenses)?