Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex depo
sited 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?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).
Start by writing out w in terms of x. After one year, there is 1.08*x dollars in the account. x dollars are then deposited, giving us a total of 1.08*x + x (normally we would simplify this to 2.08 but looking at the answers this is not a good idea.) Next, multiply by 1.08 to account for the 2nd year's interest. This brings to total to w = 1.08(1.08*x + x) = (1.08^2)*x + 1.08*x. Factoring out x, we are left with w = (1.08^2 + 1.08) * x. Dividing both sides by (1.08^2 + 1.08), we are left with x = w/(1.08^2 + 1.08) so the answer is d.
