Answer:
1) The market interest rate is 5% and the bonds issue at face amount.
Dr Cash 1,300,000
Cr Bonds payable 1,300,000
Year Interest payment Book value of bonds
June/1 $32,500 $1,300,000
Dec/1 $32,500 $1,300,000
June/2 $32,500 $1,300,000
2) The market interest rate is 6% and the bonds issue at a discount.
price of bonds:
PV of face value = $1,300,000 / (1 + 3%)³⁰ = $535,582.79
PV of coupons = $32,500 x 19.600 (PV annuity factor, 3%, 30 periods) = $637,000
market price = $1,172,582.79
Dr Cash 1,172,582.79
Dr Discount on bonds payable 127,417.21
Cr Bonds payable 1,300,000
discount amortization per coupon payment = $127,417.21 / 30 = $4,247.24
Year Cash paid Interest Amortization Bond Book
expense bond discount discount value
June/1 $32,500 $36,747.24 $4,247.24 $123,169.97 $1,176,830.03
Dec/1 $32,500 $36,747.24 $4,247.24 $118,922.73 $1,181,077.27
June/2 $32,500 $36,747.24 $4,247.24 $114,675.49 $1,185,324.51
3. The market interest rate is 4% and the bonds issue at a premium.
price of bonds:
PV of face value = $1,300,000 / (1 + 2%)³⁰ = $717,692.16
PV of coupons = $32,500 x 22.396 (PV annuity factor, 2%, 30 periods) = $727,870
market price = $1,445,562.16
Dr Cash 1,445,562.16
Cr Bonds payable 1,300,000
Cr Premium on bonds payable 145,562.16
discount amortization per coupon payment = $145,562.16 / 30 = $4,852.07
Year Cash paid Interest Amortization Bond Book
expense bond discount premium value
June/1 $32,500 $27,647.93 $4,852.07 $140,710.09 $1,440,710.09
Dec/1 $32,500 $27,647.93 $4,852.07 $135,858.02 $1,435,858.02
June/2 $32,500 $27,647.93 $4,852.07 $131,005.95 $1,431,005.95
