Question

Ou have $11,122.76 in a brokerage account, and you plan to deposit an additional $4,000 at the end of every future year until your account totals $210,000. you expect to earn 12% annually on the account. how many years will it take to reach your goal?

Answer 1

This one is tricky, only because you aren't sure if they are adding the percentage before you deposit 4,000 more, or after.  Since both are annually.
But I would add 11,122.76 and 4,000 =15,122.76 add 12% which is 1814.73 making your total for the first year = 16,937.49. 

Then assume it again, you add 4,000.  That's 20,937.49

add 12% of 20,937.49 which is 2512.50 so that equals =23,449.99 by the end of year 2.

so add 4,000 again, that's 27,449.99

find 12% and add it to get =3294 add that to the total =30,743.99 by year 3.

(I'm sure they want you to round, which I keep doing with my decimals, but it'll probably go faster if you round ahead of time, but I'm trying to be accurate)

Keep going....

34,743.99 which 12% added is 4169 or a total of $38,912.99 by end of year 4.

add 4,000 to get =42,912.99 and 12% that's roughly a total of 48,063 rounded by the end of year 5.

52,063  at 12% 58,310 by year 6.

58,000 add 12% = 64,960 at end of year 7
68,960 add 12%= 77235 at year 8

81,235 add 12% =90,983 by year 9

94,983 add 12% =106,380 by year 10 (this is where you can assume that they'd want you to double it and it's be 20 years and 210,000.  But in real math, the amount is increasing so much because it's 12% of the current balance)

123,626.56 year 11

142,942 by year 12

164,574 by year 13

188,803 by year 14

203, 939 by year 15

So you'd go over 210 by year 16.

Now again, this depends if they add the 12% before or after you deposit 4,000 each year.  It also has to have an easier equation, but to be accurate I did it this way.  I'm sure that they want you to do like x=years and you'd go 11,122.76+4,000 multiplied by 12% and then try different years to see the number you get until you'd come to 16.