A couple thinking about retirement decide to put aside $$24,000$ each year in a savings plan that earns $9\mathrm{.}40\%$ interest. In $8$ years they will receive a gift of $$74,000$ that also can be invested.

a$.$ How much money will they have accumulated $16$ years from now? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Accumulated savings

b$.$ If their goal is to retire with $$1,413,897$ of savings, how much extra do they need to save every year? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Additional savings

per year