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a ) A man wants to retire at age 6 5 and be able to draw $ 1 0 , 0 0 0 a year
a A man wants to retire at age and be able to draw $ a year from retirement savings
to supplement his Social Security income and employee retirement benefits. At retirement
he anticipates investing his savings in government securities that should return a year
compounded continuously. By repeating the arguments that led to equation show
that after retirement the principal in his account satisfies the ODE
where we have used units of $
b Determine the general solution of and find a formula for the solution with, as yet
undetermined, initial value
c How large must the man's initial retirement savings be so that he can continue drawing his
$ income annuity for years?
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