Consider the expressions given in question 2a and 2b below, interpreting each as the total value of a savings account into which you have been depositing $200 each year on January 1 (starting on January 1, 2011), and which compounds 5% interest annually on December 31 of each year.

For each of the following expressions, describe when (i.e. on what date or range of dates) the account value would equal each of the following expressions. Consider again the expression in question 2a above. The term ($200)(1.05)³ is the future value of the deposit made on what date?

2a. ($200)(1.05)⁴ + ($200)(1.05)³ + ($200)(1.05)² + ($200)(1.05)¹

2b. ($200)(1.05)⁴ + ($200)(1.05)³ + ($200)(1.05)² + ($200)(1.05)¹ + $200