You have $\backslash (\backslash$$ $30,000\backslash )$ that you would like to invest today. Beginning one year from today, you also plan to invest $\backslash (\backslash$$ $15,000\backslash )$ per year for $40$ years until you retire at that point. You plan on living for $20$ years after retiring. If interest rates are $7$ percent, what size annual annuity payment can you expect for your retirement years? $($All annuity payments are at year$-$end.$)$

Multiple Choice

$\backslash$$$220,504$

$\backslash$$$165,440$

$\backslash$$$325,067$

$\backslash$$$377,076$

$\backslash$$$250,900$