Stefani$$ German, a$40-$year$-$old woman, plans to retire at age$65,$ and she wants to accumulate $$$$490$ comma $000$ over the next $25$ years to supplement the retirement programs provided by the federal government and her employer. She expects to earn an average annual return of about $4\%$ by investing in a$$ low$-$risk portfolio containing about $20\%$short$-$term securities$,30\%$ common$$ stock, and $50\%$ bonds.

Stefani currently has $$$$56$ comma $268$ that at an annual rate of return of $4\%$ will grow to about $$$$150$ comma $000$ by her $65$th birthday$($the $ $150$ comma $000$ figure is found using time value of money$$ 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 $$$$24\mathrm{.}01$ each$$ year, she will accumulate$$ $$1,000$ by age $65.$ Saving $5$ times that amount each$$ year, $ $120\mathrm{.}05,$ allows Stefani to accumulate roughly$$ $$5,000$ by age $65.$

a$.$ How much additional money does Stefani need to accumulate over time to reach her goal of $$$$490$ comma $000?$

b$.$ How much must Stefani save to accumulate the sum calculated in part a over the next $25$years$?$Stefani German, a $40-$year$-$old woman, plans to retire at age $65,$ and she wants to accumulate $$490,000$ 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 $4\%$ by investing in a low$-$risk portfolio containing about $20\%$

short$-$term securities$,30\%$ common stock, and $50\%$ bonds.

Stefani currently has $$56,268$ that at an annual rate of return of $4\%$ will grow to about $$150,000$ by her $65$ th

birthday $($the $$150,000$ 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 $$24\mathrm{.}01$ each year, she will accumulate $$1,000$ by age $65.$ Saving $5$

times that amount each year, $$120\mathrm{.}05,$ allows Stefani to accumulate roughly $$5,000$ by age $65.$

a$.$ How much additional money does Stefani need to accumulate over time to reach her goal of $$490,000?$

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 $$490,000,$ Stefani needs to accumulate $$340000.($Round to the nearest dollar.$)$

b$.$ To accumulate the sum calculated in part a over the next $25$ years, the amount Stefani must deposit annually is

$$,($Round to the nearest cent.$)$