Predict next month's loan balance from historical data
You have quick and easy but rough predictions:


The "meteo method": next month will be the same as last month. No as bad as you may think, and you can even replace last month by an average of the last 6 month.
Linear regression: the meteo method will fail if there is a constant growth. Make a linear regression in function of time $x(t) = a \cdot t + b$. Your forecast will be $x(today+1)$.
Exponential regression: use a regression on a growth in percentage (exponential growth). You can find the best $a$, $b$ fitting $x(t) = a \exp(b \cdot t)$, or the best $c$, $d$ to fit $log(x(t)) = c \cdot t + d$. These are the same formula in disguise and you can use a linear regression for the last one (fit $y(t) = log(x(t))$ instead of $x(t)$). 

Note that this a "scientific" version of you method 1.
Exponential smoothing: It is an average giving more weight to the last values. There is a technical trick that makes computation specially easy if you have to forecast every month. In reference with the wikipedia page, take $\alpha = 1/6 = 0.1667$ for a 6 month history.

In the future, you will ba able to add a trend (Double exponential smoothing) and a seasonality (Holt-Winter model).


I would avoid method 2, consisting in adding forecast of individual account. This method works when every thing is linear so that errors cancel each others. When the the process is not linear, you'll have a systematic bias which will add together.

I also mention that your main challenge will more probably be the seasonality than the main trend.