For the first year, Bob gets 12% on his first deposit: 1.12(5000). The second year, Bob adds 5000 and gets 12% on top of what he had at the end of the first year plus his extra 5000 deposit: 1.12(1.12(5000) + 5000), if you expand this you get 1.12*1.12*5000 + 1.12*5000.
You can see a pattern here, so let's factor out the 5000 and see what the full 8 years would be:
5000(1.12^8 + 1.12^7 + ... + 1.12^2 + 1.12). Everything in the parentheses comes to approx. 14.775656, multiplied by 5000 gives you 73,878.28.
So D) $73,878 is your answer.
