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Part $1$

An initial investment amount$$ P$,$ an annual interest rate$$ r$,$ and a time t are given. Find the future value of the investment when interest is compounded$($a$)$ annually,$($b$)$ monthly,$($c$)$ daily, and$($d$)$ continuously. Then find$($e$)$ the doubling time T for the given interest rate.

P$=$$$25,000,$ r$=2\mathrm{.}9\%,$ t$=42$ months