Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?  Choose the correct option.
A) w/(1+1.08) B) w/(1.08+1.16) C) w/(1.16+1.24) D) w/(1.08+1.08^2) E) w/(1.08^2+1.08^2)
Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --&gt; x(1.08^2+1.08)=w --&gt; x=w/(1.08+1.08^2).   Answer: w/(1.08+1.08^2).
<result>D</result>
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?