Your payoff amount is just your current balance + (daily per diem x number of days since last payment). You are paying off current balance + accrued interest. If you call your lender they should be able to quote you a 15 day payoff.
To get a payoff letter, ask your lender for an official payoff statement. Call or write to customer service or make the request online. While logged into your account, look for options to request or calculate a payoff amount, and provide details such as your desired payoff date.
First, you'll need to contact your lender and let them know you want the information. Depending on your lender, you may have to sign in to an online account, call a helpline, or send a formal letter to start the request process.