Question

A ten-year 5% bond with semiannual coupons is purchased to yield 6% compounded semiannually.

The par value and redemption value are both $1,000. What is the book value of the bond six years after issue of the bond?

A.    Less than $960

B.    At least $960, but less than $965

C.    At least $965, but less than $970

D.    At least $970, but less than $975

E.    At least $975

Answer 1

Book value of bond in 6 years after issue is $ 965.

Hence option “At least $ 965, but less than $ 970” is correct answer.

Bond amortization schedule for six years:

Issue price of bond = Coupon amount x PVIFA (3 %, 20) + Face value x PVIF (3 %,20)

                                = ($ 1,000 x 0.025 x 14.877) + ($ 1,000 x 0.553675754186335)

                                = ($ 25 x 14.8774748604555) + $ 553.675754186335

                                = $ 371.936871511388 + $ 553.675754186335

                               = $ 925.612625697722 or $ 925.61

Bond is selling at discount.

Discount Amount = $ 1,000 - $ 925.61 = $ 74.39

Bond Amortization schedule:

A	B	C	D	E	F	G
Period (semiannual)	Interest payment 0.025 x $1,000	Interest expense G x 0.03	Amortization of bond Discount C-B	Balance in bond discount	Bonds payable	Book value of Bond F-E
0				$74.39	$1000	$925.61
1	$25	$27.7683	$2.7683	$71.6217	$1000	$928.3783
2	$25	$27.851349	$2.851349	$68.77035	$1000	$931.2296
3	$25	$27.93688947	$2.936889	$65.83346	$1000	$934.1665
4	$25	$28.02499615	$3.024996	$62.80847	$1000	$937.1915
5	$25	$28.11574604	$3.115746	$59.69272	$1000	$940.3073
6	$25	$28.20921842	$3.209218	$56.4835	$1000	$943.5165
7	$25	$28.30549497	$3.305495	$53.17801	$1000	$946.822
8	$25	$28.40465982	$3.40466	$49.77335	$1000	$950.2267
9	$25	$28.50679962	$3.5068	$46.26655	$1000	$953.7335
10	$25	$28.6120036	$3.612004	$42.65454	$1000	$957.3455
11	$25	$28.72036371	$3.720364	$38.93418	$1000	$961.0658
12	$25	$28.83197462	$3.831975	$35.1022	$1000	$964.8978