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On June 30, 2019, Gaston Corporation sold $890,000 of 11% face value bonds for $846,780.44. On...

On June 30, 2019, Gaston Corporation sold $890,000 of 11% face value bonds for $846,780.44. On December 31, 2019, Gaston sold $470,000 of this same bond issue for $493,261.83. The bonds were dated January 1, 2019, pay interest semiannually on each December 31 and June 30, and are due December 31, 2026. Required: Compute the effective yield rate on each issuance of Gaston's 11% bonds. Click here to access the tables to use with this problem. Round your answers to the nearest whole percentage.

June 30, 2019 issuance: %

December 31, 2019 issuance: %

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Answer #1
Computation of effective yield rate or effective interest rate
1 For bond June 30, 2019
We need to calculate the effective interest rate by trial and error method by taking two difference interest rate, since the coupon payments are twice year we need to divide the coupon rate, effective interest rate and life of the bond by 2 for computation purpose
Answer for the bond issued on June 30, 2019 is 12%
Answer for the bond issued on December 31, 2019 is 10%
Interest payment date Period Cash flow Present value of cash flow @ 5% Present value of cash flow @ 6%
A B Cash flow D=C/(1+5%)^A D=C/(1+5%)^A
June 30,2019 0                                 846,780                                        846,780                                        846,780
December 31, 2019 1                                 (48,950)                                        (46,619)                                        (46,179)
June 30,2020 2                                 (48,950)                                        (44,399)                                        (43,565)
December 31, 2020 3                                 (48,950)                                        (42,285)                                        (41,099)
June 30,2021 4                                 (48,950)                                        (40,271)                                        (38,773)
December 31, 2021 5                                 (48,950)                                        (38,354)                                        (36,578)
June 30,2022 6                                 (48,950)                                        (36,527)                                        (34,508)
December 31, 2022 7                                 (48,950)                                        (34,788)                                        (32,555)
June 30,2023 8                                 (48,950)                                        (33,131)                                        (30,712)
December 31, 2023 9                                 (48,950)                                        (31,554)                                        (28,973)
June 30,2024 10                                 (48,950)                                        (30,051)                                        (27,333)
December 31, 2024 11                                 (48,950)                                        (28,620)                                        (25,786)
June 30,2025 12                                 (48,950)                                        (27,257)                                        (24,327)
December 31, 2025 13                                 (48,950)                                        (25,959)                                        (22,950)
June 30,2026 14                                 (48,950)                                        (24,723)                                        (21,651)
December 31, 2026 15                                 (48,950)                                        (23,546)                                        (20,425)
December 31, 2026 15                               (890,000)                                      (428,105)                                      (371,366)
                              (777,470)                                        (89,409)                                                (0)
Interest payment date Period Cash flow Present value of cash flow @ 5% Present value of cash flow @ 6%
A B Cash flow D=C/(1+5%)^A D=C/(1+5%)^A
December 31, 2019 0                                 493,262                                        493,262                                        493,262
June 30,2020 1                                 (25,850)                                        (24,619)                                        (24,387)
December 31, 2020 2                                 (25,850)                                        (23,447)                                        (23,006)
June 30,2021 3                                 (25,850)                                        (22,330)                                        (21,704)
December 31, 2021 4                                 (25,850)                                        (21,267)                                        (20,476)
June 30,2022 5                                 (25,850)                                        (20,254)                                        (19,317)
December 31, 2022 6                                 (25,850)                                        (19,290)                                        (18,223)
June 30,2023 7                                 (25,850)                                        (18,371)                                        (17,192)
December 31, 2023 8                                 (25,850)                                        (17,496)                                        (16,219)
June 30,2024 9                                 (25,850)                                        (16,663)                                        (15,301)
December 31, 2024 10                                 (25,850)                                        (15,870)                                        (14,435)
June 30,2025 11                                 (25,850)                                        (15,114)                                        (13,617)
December 31, 2025 12                                 (25,850)                                        (14,394)                                        (12,847)
June 30,2026 13                                 (25,850)                                        (13,709)                                        (12,119)
December 31, 2026 14                                 (25,850)                                        (13,056)                                        (11,433)
December 31, 2026 14                               (470,000)                                      (237,382)                                      (207,881)
Present value of cash flow                                                 0                                          45,105
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