On April 17, 2016, you deposit $500 into a bank account that pays 3% interest compounded annually. You do the same every year – i.e., depositing $500 on April 17 – for the next 50 years. (You may assume that April 17 is also the date on which the bank pays the interest each year.)

a. On what range of dates is the balance of your account equal to $500? (Recall from two assignments ago that a “range of dates” looks like “March 21, 1999 through July 3, 2002”. That’s not the answer to this question, but a correct answer will have that form.)

b. On what range of dates is the balance of your account equal to:

$500 + $500(1.03)

c. On what range of dates is the balance of your account equal to:

 $500 + $500(1.03) + $500(1.03)2 + $500(1.03)3 + $500(1.03)4

d. Each term in the sum in 4c is the future value of the contribution made on some date – i.e., $500 is the future value of the deposit made on April 17 of some year, $500(1.03) is the future value of the deposit made on April 17 of some other year, etc. During the range of dates you gave in part c, one of the deposits has grown to $500(1.03)2. On what date was that deposit made?