You have $$20,000$ available for investment. How much money would you have in your account at the end of $10$ years, given the following

scenarios:

a$)$ You invest in an account with $3\%$ interest per year compounded semi$-$annually for a period of $10$ years.

b$)$ You invest in an account with $2\mathrm{.}9778\%$ interest per year compounded semi$-$annually for a period of $10$ years. At the end of each year,

you withdraw $$1000$ from the account.

c$)$ You invest in an account with $2\mathrm{.}9778\%$ interest per year compounded semi$-$annually for a period of $10$ years. How much you have to

withdraw annually to have nothing left at the end of the period of $10$ years?