Problem 1

How long will it take for a certain sum of money to double if the rate of interest is 6%?

 a) 8 years
 b) 10 years
 c) 11 years
 d) 12 years

( Hint: Apply the rule of 72 )

Problem 2

A very large group of bankers are asked to choose, simultaneously, a number between 0 to 200 such that the person who chooses a number that is exactly 60% of the average number chosen by the entire group gets a million dollars. If an exact answer is not found the game continues on for the next round. After every round, if an exact answer is not found, then each one is made aware of the numbers picked by others. If the game is played for a long time (and if an optimal response is defined as a result when the individuals cannot benefit any longer by changing their actions based on the response of the other members and hence no single individual gets a million dollars) then:

a)  all members of the group will reach an optimal response;
b)  some members of the group will reach an optimal response;
c)  an optimal response for this game does not exist;
d)  the game will be truncated (yield an exact result for one individual) after a
     certain number of rounds;

Problem 3

In the above problem (Problem 2) the optimal response of the group (that is the number picked by everyone in the group), if it exists, will be:

a) 0
b) 30
c) 60
d) Optimal response does not exist and the game is truncated after a 60 rounds;
e) Optimal response does not exits and the game is truncated after 30 rounds;

( Hint: the game in Problem 2 will reach a Nash equilibrium. To solve it one doesn't need math but logical reasoning ).

Problem 4

You are asked to price a certain accident insurance policy and you know nothing about insurance business or how to price insurance policies. But you are brighter than your boss. You study the claims record for the last ten years and observe that each year on an average one out of 5,000 policies has resulted in a claim of $500,000, one of out 1,000 polices have resulted in a claim of $100,000, one out of 200 policies has resulted in a claim of $10,000 and remainder of the policies have generated no claims. Thus, based solely on your observation you will price the accident insurance policy with an annual premium of:

a) $100
b) $250
c) $375
d) $875
e) None of the above;

(Hint: look for the expected value.)

Problem 5

A game of coin tossing is played such that if heads turn up in the first toss you get $2, if heads turn up in the second toss you get $4 and if heads turn up in the third toss you get $8. You win as soon as the heads turn up and the game is truncated. If this game goes on for a very long time (say, billions of tosses), the expected value of this game will be:

a) 0
b) 1
c) 2
d) infinity.

( Hint: Refer to St. Peter's paradox .)

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