Question

how to solve for interest annuity

Problem 10-1AA Computing bond price and recording issuance LO C2, P1 Hartford Research issues bonds dated January 1that pay interest semiannually on June 30 and December 31. The bonds have a $25,000 par value and an annual contract rate of 10% and they mature in 10 years, (Table BI Table B2 Table B , and Table B4 (Use appropriate factoris) from the tables provided. Round all table values to 4 decimal places, and use the rounded table values in calculations. Round your "Present Value" answers to the nearest whole dollar amount.) Required: Consider each of the following three separate situations 1. The market rate at the date of issuance is 8% (a) Complete the below table to determine the bonds Issue price on January 1. (b) Prepare the journal entry to record their issuance. 2. The market rate at the date of issuance is 10% (a) Complete the below table to determine the bonds' Issue price on January 1. (b) Prepare the journal entry to record their issuance. 3. The market rate at the date of issuance is 12% (a) Complete the below table to determine the bonds' Issue price on January 1. (b) Prepare the journal entry to record their issuance. Complete this question by entering your answers in the tabs below. Req1A Req 1B Reg 2A Req 2B Reg 3A Req 38 Complete the below table to determine the bonds' issue price on January 1, if the market rate at the date of issuance is 8%. Table values are based on: 2020 Cash Flow Table Value Amount Present Par (maturity) 0.45645 0 S value 11.410 Interest $ 1.250 16.988 (annuity) Price of bonds $ 28.397

Answer 1

The price of the bond is present value of all future cash flows

Present Value Factor (PVF) = 1 / [(1+ i)^n]

Annuity Factor (PVAF) = Sum of PVF(i, n Periods)

Where the Interest are receivable semi annually, the discounting rate becomes half the annual rate and the period is multiplied by 2.

In the Given Case,

Face Value of Bond = $ 25000

Semi Annual Interest = 25000 x 10%/2 = $ 1250

No. Of periods (n) = 2 x 10 = 20 periods

Discounting rate (semi annual) (i) = Market rate of Interest / 2

Calculating Present Value of Bond in Various Cases (Using Annuity)

Particulars	Cash Flows	Case 1		Case 2		Case 3
		(i = 4%)	Disc. Cash flows @ 4%	(i = 5%)	Disc. Cash flows @ 5%	(i = 6%)	Disc. Cash flows @ 6%
Maturity [Disc. @ PVF (i, 20th)]	25000	0.4564	11410.00	0.3769	9422.50	0.3118	7795.00
Interest [Using Annuity @ PVAF (i, 20)]	1250	13.5904	16988.00	12.4620	15577.50	11.4700	14337.50
Price Of the Bond			$28,398.00		$25,000.00		$22,132.50

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Proof of Above answer

Calculating Present Value of Bond in Various Cases (For each Period)

Years	Cash Flows	Case 1		Case 2		Case 3
		PVF @ 4%	PV of Cash Flow @ 4%	PVF @ 5%	PV of Cash Flow @ 5%	PVF @ 6%	PV of Cash Flow @ 6%
1	1250	0.9615	1201.88	0.9524	1190.50	0.9434	1179.25
2	1250	0.9246	1155.75	0.9070	1133.75	0.8900	1112.50
3	1250	0.8890	1111.25	0.8638	1079.75	0.8396	1049.50
4	1250	0.8548	1068.50	0.8227	1028.38	0.7921	990.13
5	1250	0.8219	1027.38	0.7835	979.38	0.7473	934.13
6	1250	0.7903	987.88	0.7462	932.75	0.7050	881.25
7	1250	0.7599	949.88	0.7107	888.38	0.6651	831.38
8	1250	0.7307	913.38	0.6768	846.00	0.6274	784.25
9	1250	0.7026	878.25	0.6446	805.75	0.5919	739.88
10	1250	0.6756	844.50	0.6139	767.38	0.5584	698.00
11	1250	0.6496	812.00	0.5847	730.88	0.5268	658.50
12	1250	0.6246	780.75	0.5568	696.00	0.4970	621.25
13	1250	0.6006	750.75	0.5303	662.88	0.4688	586.00
14	1250	0.5775	721.88	0.5051	631.38	0.4423	552.88
15	1250	0.5553	694.13	0.4810	601.25	0.4173	521.63
16	1250	0.5339	667.38	0.4581	572.63	0.3936	492.00
17	1250	0.5134	641.75	0.4363	545.38	0.3714	464.25
18	1250	0.4936	617.00	0.4155	519.38	0.3503	437.88
19	1250	0.4746	593.25	0.3957	494.63	0.3305	413.13
20	1250	0.4564	570.50	0.3769	471.13	0.3118	389.75
20	25000	0.4564	11410.00	0.3769	9422.50	0.3118	7795.00
Present Value of Bond			$28398.04		$25000.06		$22132.54