You'll be charged two fares but they won't both be £2.70.
Since you've not told us where your starting from, I can't confirm a definite fare for the first journey. However your reference to a £2.70 fare suggests that you're travelling from either Zone 3 or Zone 4, using an Oyster pay as you go card, at an Off-Peak time. ('Peak' times are from 0630 to 0929 and from 1600 to 1859, Mondays to Fridays). If so, that bit's correct.
Your second journey is then charged at £2.10, irrespective of the time of day (because there's no difference for Zone 1 fares)
If you only travel at Off-Peak times (and don't go beyond Zone 4), the maximum you'll be charged for the whole day is £7.70, irrespective of the number of journeys you make. If some of your travel is at Peak times, the maximum you can be charged is £10.60.
http://www.tfl.gov.uk/tickets/14416.aspx