$2-$ Anna, a civil engineer, invests $\backslash (\backslash$$ $8,000\backslash )$ in a retirement fund today. The fund offers an $\backslash (\backslash$mathbf$\{8\backslash \%\}\backslash )$ annual interest rate, compounded annually. Additionally, Anna plans to deposit an extra $\backslash (\backslash$$ $1,000\backslash )$ at the end of each year, starting from the $2$nd year, and continue doing so for the next $18$ years.

Questions:

i$.$ What will be the total amount available in Anna's account at the end of $20$ years?

ii$.$ If Anna decides to withdraw an equal amount of money every year for the next $10$ years $($starting at the end of year $21),$ how much can she withdraw each year without exhausting the fund?

$3-$ A company plans to invest $\backslash (\backslash$mathbf$\{\backslash$$ $50,000\}\backslash )$ in a new packaging machine in $2023.$ If the project is delayed and the machine is purchased in $2026,$ the cost of money is $\backslash (\backslash$mathbf$\{8\backslash \%\}\backslash )$ per year $($compounded annually$).$

Questions:

i$.$ What is the equivalent cost of the machine if purchased in $2026?$

ii$.$ What would have been the cost of the machine if purchased in $2020?$