accumulate $$1,000$ by age $65.$ Saving $5$ times that amount each year, $$104\mathrm{.}75,$ allows Stefani to accumulate roughly $$5,000$ by age $65.$

a$.$ How much additional money does Stefani need to accumulate over time to reach her goal of $$500,000?$

b$.$ How much must Stefani save to accumulate the sum calculated in part a over the next $25$ years?

a$.$ To reach her goal of $$500,000,$ Stefani needs to accumulate $$.($Round to the nearest dollar.$)$