Using only the expected value as you have is much easier to manipulate. Taking volatility into account is a bit more intense and probably better suited for the quant stack.
If you want to determine this monthly, everything must be put in monthly terms, so the monthly rate of return on investment assuming 5% annually is
It appears as if the deposit rate grows as fast as the rate of return by your equation, so the equation can be simplified to
I * [ 1 + 0.004 + D / I ] ^ n
I is the initial investment,
D is the amount of the first month's deposit, and
n is the number of months.
When taking into account the other mathematical moments, the Variance Gamma process can be used for a realistic projection over time, but although it will be more precise, it will still be inaccurate because of the random walk.
For simplicity's sake,
0.004 can be multiplied by the standard normal random variable to account for volatility. The CDF with a standard deviation equal to the historical standard deviation of log investment will be more realistic, and using the Variance Gamma process would be even more realistic.
Then again, one could always use actual past investment monthly returns randomly chosen to simulate future returns. That might take a little more than the standard programming Excel allows.