Mr$.$ Moore is $35$ years old today and wants to set aside an equal amount at the end of each of the next $25$ years so that he can retire at age $60.$ He expects to live to the maximum age of $80$ and wants to be able to withdraw $$25,000$ per year from the account on his $61$st through $80$th birthdays. The account is expected to earn $10\%$ p$.$a$.$ for the entire period.

$($i$)$ What must be the balance in the account after $25$ years in order for Mr$.$ Moore to achieve his retirement objective?

$($ii$)$ Determine the size of the annual deposits that must be made by Mr$.$ Moore to achieve his retirement objective?

Answer both questions and explain.