In a small country with a stationary population, a special system is used for supporting the elderly.

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In a small country with a stationary population, a special system is used for supporting the elderly. On January 1, each person whose age is between 20 and 65 contributes 100 to a pool. On the same date, payments of A^ are made from the pool to all persons aged 65 and over, with the entire pool being allocated.

(a) Derive an expression for K.

(b) If A^ = 500, £20 = 2 • 45, and the complete expectation of life at age 65 is 15 years, what is the complete expectation of life at age 20?

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