During the 1st year at university, Erica¡¦s father had been sending her $1,000 per month for incidental expenses.Starting from the 2nd academic year, her father decided instead to make a
deposit into a savings account on August 1st every year so that Erica could withdraw $1,000 on the
first day of each month over the academic year from September 1st
to June 1st.
a)If the bank pays 5% p.a. interest compounded monthly, how much should Erica¡¦s father deposit every year on August 1st?
b)If the banking condition remains the same but the father wishes to deposit every year on August 31st
, will the deposit amount be the same as in part (a)? Why?

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