A pension plan is obligated to make disbursements of $2.5 million, $3.5 million, and $2.5 million at the end of each of the next
three years, respectively. The annual interest rate is 8%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
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Answer: The probabilities of winning a contract are
Let the Probability of C winning the contract - P(C) be 'X'
Then,
Probability of B winning the contract - P(B) will be '7X' and
Probability of A winning the contract - P(A) will be
Since the total of all the probabilities is 1,
So,