Assume contunious compounding and continuous payments for

the following problem.

Suppose you wish to retire in $44$ years on a fixed income equiva$-$

lent to $$27,962\mathrm{.}93$ in today's dollars, and that inflation over the

coming $44$ years averages $3\mathrm{.}5$ percent.

How much money, per month, will you need to invest starting

now, with zero initial investment, to attain the necessary nest

egg for retirement if your investment earns a $6\mathrm{.}2$ percent yield as

you invest and throughout retirement?

Round your answer to the nearest dollar.