Stefani German, a $40-$year$-$old woman, plans to retire at age $65,$ and she wants to accumulate $$400,000$ over the next $25$ years to supplement the retirement programs provided by

the federal government and her employer. She expects to earn an average annual return of about $6\%$ by investing in a low$-$risk portfolio containing about $20\%$ short$-$term securities$,$

$30\%$ common stock, and $50\%$ bonds.

Stefani currently has $$27,960$ that at an annual rate of return of $6\%$ will grow to about $$120,000$ by her $65$ th birthday $($the $$120,000$ figure is found using time value of

money techniques, Chapter $4$ Appendix.$)$ Stefani consults a financial advisor to determine how much money she should save each year to meet her retirement savings objective.

The advisor tells Stefani that if she saves about $$18\mathrm{.}23$ each year, she will accumulate $$1,000$ by age $65.$ Saving $5$ times that amount each year, $$91\mathrm{.}15,$ 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 $$400,000?$

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 $$400,000,$ Stefani needs to accumulate $$.($Round to the nearest dollar.$)$