On the day Zola turned 30 years old, she decided to make regular annual deposits into a bank with a plan to save at least $200,000 by the time she was 40. The bank would pay interest of 5% per annum, paid annually. (The interest is paid at the end of each year, on the balance of the account.) Zola went through the following steps to determine how much, $D, she would have to deposit each year to reach her goal. Each year Zola deposits the same amount.

(a) Zola makes her last deposit when she is 40. Let's call the D-Day. On D-day she aims to have$200,000. How many deposits does she make altogether?

(b) Consider only the rst deposit Zola makes - the initial one. Each year, this deposit earns interest. What is the nal value of this deposit on D-day?

(c) Consider only the second deposit Zola makes - the one after the initial one. Each year, this deposit earns interest. What is the nal value of this deposit on D-day?

(d) Let T be the nal value of the balance of Zola's account, the day after she makes her last deposit. Write down a sum that determines the value T. (We know is intended to be 200,000, but it is also determined by a formula in terms of D. It is this formula that is wanted in this part.)