for(i in 1:nrow(df)){

      df$new_column[i] <- df$column1[i] * df$column2[i]

      }

new_df <- ddply(df, .(column1,column2), transform, new_column = column1 * column2)
     # but this is taking forever

df$new_column <- df$column1 * df$column2

df <- transform(df, new = column1 * column2)

df <- within(df, new <- column1 * column2)

library(data.table)
 DT <- data.table(df)
 DT[ , new := column1 * column2]