The average fee charged by Fannie Mae and Freddie Mac to lenders rose last year, while payments collected on the Home Affordable Refinance Program contributed to the GSEs’ bottom line, according to the Federal Housing Finance Agency.The third-annual FHFA study found that the average total guarantee fee charged by Fannie and Freddie on single-family mortgages was 26 basis points in 2010, compared to 22 bps in 2009. When HARP loans were excluded, the FHFA said the total average g-fee increased to 25 bps in 2010 from 21 bps in 2009.