At age $36,$ you start saving for retirement. If your investment plan pays an APR of $4\%$ and you want to have $$$$1\mathrm{.}2$ million when you retire in $29$years$,$ how much should you deposit$$ monthly?

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Part $1$

You should invest $$$

each month.

$($Do not round until the final answer. Then round to two decimal places as$$ needed.$)$