As soon as she graduated from college, Kay began planning for her retirement. Her plans were to deposit $500 semiannually into an IRA (a retirement fund) beginning six months after graduation and continuing until the day she retired, which she expected to be 30 years later. Today is the day Kay retires. She just made the last $500 deposit into her retirement fund, and now she wants to know how much she has accumulated for her retirement. The fund earned 10 percent compounded semiannually since it was established.

a. Compute the balance of the retirement fund assuming all the payments were made on time.

b. Although Kay was able to make all of the $500 deposits she planned, 10 years ago she had to withdraw $10,000 from the fund to pay some medical bills incurred by her mother. Compute the balance in the retirement fund based on this information.