The national average mortgage rate charged for purchasing previously owned homes dropped 12 basis points to 4.62% in June, according to the Federal Housing Finance Agency. June marks the third-straight month of declines. The average rate, according to the index history, hasn’t reached above 5% since April 2010, when the homebuyer tax credit was still available. The FHFA averages rates based on a small monthly survey of lenders originating government-insured or guaranteed mortgages, refinances and balloon loans. For June, the FHFA measured more than 6,000 loans from 31 lenders. The average interest rate on a 30-year fixed-rate mortgage slid 13 bps to 4.79% in June. The initial fees and charges averaged 0.94% of the loan balance in June, up 9 bps from the month before. Of all the loans studied in June, 28% were “no-point” mortgages. The average loan period inched closer to 30 years, and the average loan-to-value ratio in June was 76.3%. The average loan amount was for $219,000, down nearly $4,000 from the month before. Write to Jon Prior. Follow him on Twitter @JonAPrior.