Answer:
the bond discount = face value - market value
market value = PV of face value + PV of coupon payments
PV of face value = $500,000 / (1 + 7%)²⁰ = $129,209.50
PV of coupon payments = $30,000 x 10.594 (PV annuity factor, 7%, 20 periods) = $317,820
market value = $447,029.50
January 1, 2017, bonds are issued at a discount
Dr Cash 447,029.50
Dr Discount on bonds payable 52,970.50
Cr Bonds payable 500,000
the discount amortization for first coupon payment = ($447,029.50 x 7%) - $30,000 = $31,292 - $30,000 = $1,292
July 1, 2017, first coupon payment
Dr Interest expense 31,292
Cr Cash 30,000
Cr Discount on bonds payable 1,292
