Mr$.$ Moore is $35$ years old today and is beginning to plan for his retirement. He 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 $10$ percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr$.$ Moore.

a$.$ $$212,850$

b$.$ $$23,449$

c$.$ $$2,164$

d$.$ $$8,514$

Show all work!!