I need the formula that answers this question??

Question

I am a stock trader who earns 3% on my account each month.

If I start with an initial investment of 100$, earn 3% growth each month, while also adding an additional 100$ to the account each month, how much would the account be worth in 20 years?

Please, supply the formula you used to reach your answer.

Answer 1

You can model this with a recursion equation. 

 

V_n = V_n-1 * (1.03) + 100 

with V₀ = 100.  Basically, the value of the account at any given month, n, is the value of the previous month multiplied by 1.03 and increased by 100.  Recursion equations are easily modeled in excel!  Try this: type in your initial value, 100, into cell A1.  In Cell A2, type =A1*1.03+100.  Drag the equation down and each cell will fill with the value for each month.  At 20 years, or 240 months, you would have $4133327.356.

Answer 2

The formula should be that of an Ordinary Annuity.  I suggest that you Google Ordinary Annuity formula.

 

(I am somewhat surprised that a stock trader needs this inquiry.)

 

3% growth per month is darned good!