Unless you didn't start the interest accrual clock until 1/9 then your payment schedule is understated.
Run a daily simple interest amortization and you will find there will be an unpaid balance of $50.60 after the 142nd payment is applied. In order to pay the balance in full, the borrower would have to pay a final payment of $160.80, not $110.20. Since you understated a payment, you also understated the TOP and FC. Using an adjusted final payment of $160.80, APRWIN will calculate an APR of 19%.
Another way to view the problem is to say that the first payment was understated by the 6 days' interest that accrued from 1/3 through 1/9. If you add that amount ($38.08) to the first payment (bringing it up to $148.28) and run APRWIN, it will calculate an APR of 19%.
The root of this problem is your loan origination calculations. Your loan origination software is computing the payment schedule that would be appropriate for a loan originated on 1/9--including 7 days' interest, not 13. Your servicing system, however, will take 13 days' interest out of the first payment. That puts the loan's amortization behind schedule and it never recovers.
The simplest way to calculate the appropriate adjustment is to load the disclosed APR and FC into APRWIN along with the adjusted payment schedule (1 @ $148.28 due 1/16, followed by 141 @ $110.20), and let it calculate a full lump sum adjustment as of the appropriate point on the payment schedule timeline.
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...gone fishing.