John Roberts has $42,180.53 in a brokerage account, and he plans to contribute an additional $5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12 percent. If John’s goal is to accumulate $250,000 in the account, how many years will it take for John to reach his goal?

Help augustleo... ::confused:

You may want to post this in the mathmatics forum. I'm sure there is an easier way to do this. However, I can tell you how to do it the long way and you do the hard work. Start with 42180.53 and muliply by 1.12, which will give you the annual gain of 12% for the first year, 47242.93. Multiply 47242.92 by 1.12 for the second years annual gain, 52911.26. I hope you see a trend growing hear. Continue this trend until you hit 250000. Just make sure you are count the years as you do the math.

the easier way would be to use n as the number of years, then raise the interest rate to the exponential of n. so it would be: I^n (I=int. rate; n=number of years)

You reach your goal at the end of the 11th year.

See Schedule:-

YEAR
1 42,180.53 47,242.19
2 52,242.19 58,511.25
3 63,511.25 71,132.60
4 76,132.60 85,268.51
5 90,268.51 101,100.73
6 106,100.73 118,832.82
7 123,832.82 138,692.76
8 143,692.76 160,935.89
9 165,935.89 185,848.20
10 190,848.20 213,749.98
11 218,749.98 244,999.98
12 249,999.98