$3.(17$ points$)$ Your retirement account $($which is expected to yield an $8\%$ return per year$)$ has a current balance of $ $5,000.$ You are going to retire in $20$ years. a$.(6$ pts$)$ How much would you need to invest each year in order to accumulate a total amount that will guarantee withdrawing $ $10,000$ annually for $30$ years starting from year $21?(15$ points$)$ Your retirement account, projected to yield an $8\%$ annual return, currently stands at $$5,000.$

With retirement planned in $20$ years, determine the annual investment required to accumulate a

sufficient amount ensuring a $$10,000$ annual withdrawal for $30$ years, starting from year $21.$

a$.(3$pts$)$ How much would you need to invest each year in order to accumulate a total amount of

$$100,000$ at the end of year $20?$

b$.(6$pts$)$ Determine the annual investment required to accumulate a sufficient amount ensuring a

$$10,000$ annual withdrawal for $30$ years, starting from year $21.$

c$.(4$pts$)$ If you decide to invest monthly, how much would you need to invest each month in order to

accumulate a total amount that will guarantee withdrawing $$10,000$ annually for $30$ years starting

from year $21?$

d$.(2$pts$)$ Compare the annual investments in part $($a$)$ with the total amount that you would invest in

one year in part $($b$)(12$ times the monthly investments$).$ Which one is greater? Why?