Now, let's discuss our third quarter results in which we achieved $0.91 in adjusted earnings per share, a 21% increase over Q3 of 2019 and adjusted EBITDA of $58 million, a 13% increase.
As for our growth metric, the average number of paid worksite employees in Q3 of 2020 increased by 1.7% sequentially over the Q2 period to 231,750, which was above the high-end of our expected range.
Now you may recall that employee layoffs in our client base drove a 6% reduction in paid worksite employees from the outset of the pandemic in March through the low point in May of this year.
Additionally, client retention for both Q2 and Q3 has remained at our historical level of 99% and worksite employees continue to be added from new client sales.
Now let's move on to gross profit, which increased by 8% over Q3 of 2019.
Now turning to operating expenses, Q3 operating expenses included continued investment in our growth, including costs associated with a 10% increase in the average number of trained business performance advisors.
The Q3 year-over-year increase in total operating expenses of 15% was impacted by increased stock-based compensation costs.
Now operating expenses excluding stock-based compensation and depreciation and amortization increased just 4.6% over Q3 of 2019.
Adjusted cash has increased from $108 million at December 31, 2019 to $213 million at September 30th, while repurchasing 1.3 million shares of stock at a cost of $91 million, paying now $47 million in cash dividends and investing $69 million in capital expenditures to-date during 2020.
Borrowings increased by $100 million over the nine months and $130 million remains available under our credit facility.
As Doug mentioned, client retention continued at historical levels of 99%, despite the economic pressure on small businesses in the current environment.
In addition, our booked sales since the pandemic have been approximately 70% of our pre-pandemic sales budget, which we believe is solid performance in a virtual selling environment.
In the third quarter, paid worksite employees from previously booked sales was 92% compared to the same period last year, demonstrating continued demand for our services and strong execution in enrolling new clients.
During this period, we virtually trained over 350 BPAs in our Level 1, 2 and 3 and our certified Business Performance Advisor programs.
Our trained BPA count increased 10% over the same period last year, positioning us well for our fall selling season.
We saw a drop in paid worksite employees of approximately 6% in two months, followed by a steady rebound over the following four months, supported by fiscal stimulus and easing restrictions.
As I mentioned last quarter, client interactions increased 300% and the average length of time of these interactions doubled.
For the fourth quarter, we are forecasting average paid worksite employees in a range of 236,500 to 238,500, a sequential increase of 2% to 3% over Q3 of 2020.
This equates to an expected decrease in average paid worksite employees of only 1% for the full year 2020 in the face of significant challenges for the small business community caused by the pandemic and its impact on the economy.
With an improved outlook for Q4 worksite employee growth, our current pricing strength and a range around expectations in our direct cost programs, particularly our benefits program, we're now forecasting Q4 adjusted EBITDA of $21 million to $30 million and adjusted earnings per share of $0.20 to $0.38.
When combined with our Q3 outperformance, we're raising our full year 2020 earnings guidance and now forecasting adjusted EBITDA of $271 million to $281 million, an increase of 8% to 12% when compared to 2019.
As for full year 2020 adjusted EPS, we are now forecasting a range of $4.35 to $4.53, up from our previous guidance of $3.67 to $4.04.

Summary:
Now, let's discuss our third quarter results in which we achieved $0.91 in adjusted earnings per share, a 21% increase over Q3 of 2019 and adjusted EBITDA of $58 million, a 13% increase.
Borrowings increased by $100 million over the nine months and $130 million remains available under our credit facility.
When combined with our Q3 outperformance, we're raising our full year 2020 earnings guidance and now forecasting adjusted EBITDA of $271 million to $281 million, an increase of 8% to 12% when compared to 2019.
As for full year 2020 adjusted EPS, we are now forecasting a range of $4.35 to $4.53, up from our previous guidance of $3.67 to $4.04.