The amount that should be reported on December 31 as bond liability is $35,883.33.
To calculate the bond liability on December 31:
Calculate the original carrying value:
Face value = $100,000
Stated interest rate = 10%
Maturity = 10 years
Market rate on interest = 10% (on January 1)
Since the market interest rate is equal to the stated interest rate on January 1, the original carrying value is equal to the face value:
Original carrying value = Face value = $100,000
Calculate the change in fair value due to interest rate change:
Market interest rate increase = 11% - 10% = 1%
Bond maturity remaining = 9 years (10 years - 1 year)
Using the present value of an annuity factor, calculate the present value of the remaining interest payments at the new market rate:
Present value of interest payments = Face value * Coupon rate * Present value of an annuity factor for 9 years at 11%
Present value of an annuity factor for 9 years at 11% = 6.495
Present value of interest payments = $100,000 * 0.10 * 6.495 = $64,950
Calculate the change in fair value due to time passage:
Coupon payment = Face value * Coupon rate = $100,000 * 0.10 = $10,000
Interest income accrued = Coupon payment * Time passed = $10,000 * (1 year / 12 months) = $833.33
Calculate the adjusted carrying value:
Adjusted carrying value = Original carrying value + Change in fair value due to interest rate change + Change in fair value due to time passage
Adjusted carrying value = $100,000 - $64,950 + $833.33 = $35,883.33
Therefore, the amount that should be reported on December 31 as bond liability is $35,883.33.