With regard to example 10.2 (b). I am not sure why we are dividing by s bar and why we approximate it by s_(54.5)

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Part (b) of the question states that the $100 000 given is the "rate" of salary at age 55, as opposed to part (a) which states that the $75 000 was the salary received over the year leading up to age 35. This is you should use s bar which is the symbol for the salary rate.

If you consider the relationship between the definitions of the salary rate and the salary scale on a previous page in the textbook, you will see that the approximation of s bar using s is intuitive.

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