Jeanne and Harold Kimura want to set up a TDA that will generate sufficient interest at maturity to meet their living expenses, which they project to be $$850$ per month. $($Round your answers to the nearest cent.$)$

$($a$)$ Find the amount needed at maturity to generate $$850$ per month interest if they can get $6\frac{1}{2}\%$ interest compounded monthly.

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$($b$)$ Find the monthly payment that they would have to put into an ordinary annuity to obtain the future value found in part $($a$)$ if their money earns $8\frac{1}{4}\%$ and the term is twenty years.

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