Can you deduct interest paid to your father on your personal income taxes? Interest paid on passive investments can be deducted from the amount earned by that investment as an investment expense as long as the amount earned is greater than the total paid for the interest expense. Also beware if the amount of interest paid is greater than the yearly gift tax exclusion, as the IRS might interpret this as a creative way of giving gifts to your father without paying gift tax.
Do you pay taxes on the interest you pay? No, because is an expense, not income, you would not count interest paid to him as taxable income.
Does your father owe taxes on the interest he collects from you? Yes, that is income to him.
And the last question you didn't ask, but I expect it is implied: Do you owe taxes on the quarterly profits? Yes, that is income to you.
The Forbes article How To Arrange A Loan Between Family Members is a bit dated, but still a good source of information. You really should write a formal note (signed by both you and your father) indicating the amount borrowed, the interest rate you are paying on that amount, and when the loan will be repaid. If your father has set the interest rate too low, this could also be considered a gift to you, though we would really be talking about large amounts of money to hit the gift tax limit on interest alone.