please show your works

2. Joe negotiates a $50,000 mortgage on a house with semiannual payments of $3,000 for the first year, $3,500 for the second year, $4,000 for the third year, increasing similarly until the final payment. The first payment is due 6 months after the loan. The annual effective interest rate is 10%. Find the outstanding balance to the nearest $500 immediately after the 4th payment. (A) $45,000 (B) $45,500 (C) $46,000 (D) $46, 500 (E) $47,000