September $18,2024$

finanace$02$ay

Assume contunious compounding and continuous payments for

the following problem.

Suppose you wish to retire in $42$ years on a fixed income equiva$-$

lent to $$62,385\mathrm{.}32$ in today's dollars, and that inflation over the

coming $42$ years averages $2\mathrm{.}9$ 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 $7\mathrm{.}8$ percent yield as

you invest and throughout retirement?

Round your answer to the nearest dollar.