I can help with the formula for excel, but I have to say that YNAB is much more sophisticated than that, and for £14.99 (at the moment) it's worth it.
Anyway, formulas:
If you had the following set up:
Column A: Incomings
Column B: Outgoings
Column C: Balance
Row1, Column C: Starting balance
Rows 2 and onwards: Incomings/Outgoings/Balances
To get cell C2 (The balance after you've added anything that's come into the account and deducted anything that's gone out of the account since the starting balance) to calculate, you should type in:
=SUM(C1+A2-B2)
That is saying: "Take the starting balance, add on any incomings and deduct any outgoings".
The next balance would be =SUM(C2+A3-B3), the next =SUM(C3+A4-B4) and so on. The easiest way to achieve that is to highlight the cell with the formula in it, highlight a big block of cells directly below it, then paste. It means that as you type values in to the cells on each row, it will automatically calculate what the remaining balance is.