Wesley and Dottie Turner have a new$$ grandchild, William. They want to create a trust fund for him that will yield $$$$290,000$ on $25$th birthday.

a$)$ What lump sum would they have to deposit now at $5\mathrm{.}4\%,$ compounded$$ continuously, to achieve $$$$290,000?$

b$)$ Wesley and Dottie decide instead to invest a constant money stream of$$ R$($t$)$ dollars per year. Find$$ R$($t$)$ such that the accumulated future value of the continuous money stream is $$$$290,000,$ assuming an interest rate of $5\mathrm{.}4\%,$ compounded continuously.

a$)$ To achieve $$$ $290,000,$ they would have to deposit $$$

b$)$ To achieve $$$$290,000,$ they would need a constant money stream of $$$ per year