Does refinancing help?

Keep current loan
  Balance today        = $17,289.14
  Monthly rate r       = 18% ÷ 12 = 1.5%
  Month 1 interest     = $17,289.14 × r = $259.34; principal = $507.87 − interest = $248.53
  Paying $507.87 a month clears the balance in 48 months (last payment $507.76)
  Total of payments    = $24,377.65;  interest = $7,088.51;  cost from today = $7,088.51

Refinance: 10% for 60 months
  Payoff needed        = balance $17,289.14 + penalty $0.00 = $17,289.14
  Amount financed      = $17,289.14 (no fee)
  Monthly rate r       = 10% ÷ 12 = 0.833333%
  Payment              = amount × r × (1+r)^n ÷ ((1+r)^n − 1) = $17,289.14 × 0.00833333 × 1.645309 ÷ 0.645309 = $367.34
  Total of payments    = 367.3431 × 60 = $22,040.59
  Cost from today      = $22,040.59 − $17,289.14 = $4,751.45  (interest $4,751.45 + fees and penalty $0.00)
  Estimated APR        = the annual rate at which 60 payments of $367.34 are worth $17,289.14 today = 10.00%
  Difference           = $4,751.45 − $7,088.51 = −$2,337.06
  Break-even           = first month where cost so far under the new loan is at or below the old loan and stays there: from day one

Refinance, keep paying $507.87
  Same $17,289.14 at 10%, paid at $507.87 a month, clears in 41 months
  Total of payments    = $20,418.33;  cost from today = $3,129.19;  versus keeping the old loan: −$3,959.32

Cost so far after m payments = payments made + balance still owed − balance today. Fees on the old loan were paid long ago and are ignored on both sides.

1. Current lender: what is my exact payoff amount as of today, how much interest accrues per day, and is there any prepayment penalty? I used $17,289.14 and no penalty.
2. New lender: what APR is on the Truth in Lending disclosure, and does it include every fee? I estimate about 10.00%.
3. New lender: can I get the same 10% rate on a 48-month term, so my payoff date does not move?
4. New lender: is this loan simple interest with no prepayment penalty, so that paying $507.87 a month instead of $367.34 goes straight to principal?
5. New lender: does the rate depend on autopay or on opening an account, and what happens if I cancel?

• Your balance today is the payoff amount. Accrued interest between statements, late fees and escrow are not included unless you add them to the balance.
• Both loans charge simple interest monthly on the remaining balance, with every payment on time and in full.
• Fees you already paid on your current loan are sunk and ignored on both sides. Only future money counts.
• Estimated APR comes from a regular-period cash-flow calculation on the terms you entered. The lender's disclosure is the authoritative figure.
• This is an offer you typed in. We do not know whether any lender would approve you for it, and we do not recommend one.