Input | Output |
---|---|
![]() Calculate the value of bond D shown in the following table, all of which pay interest semiannually. <image 1> | The correct answer is $1,245.99. First, calculate the semiannual coupon payment: 70 Next, calculate the number of semiannual periods: 10 years x 2 = 20 periods Then, calculate the present value of the coupon payments using the formula: PV = C x [1 - (1 + r)^-n] / r where: C = semiannual coupon payment r = semiannual interest rate n = number of semiannual periods PV = 70 x [1 - (1.05)^-20] / 0.05 PV = 70 x 0.62311 / 0.05 PV = $872.35 Finally, calculate the present value of the bond: PV of bond = PV of coupon payments + PV of principal PV of bond = 1,000 PV of bond = $1,872.35 Therefore, the value of bond D is $1,872.35. Expected Answer: 1249 Difficulty: Medium Subfield: Managerial Finance |
{ "id": "gen-YhqN5erpvGrZrdet0pB4wKBaVjO7", "model": "google/gemini-pro-vision", "choices": [ { "message": { "role": "assistant", "content": " The correct answer is $1,245.99.\n\nFirst, calculate the semiannual coupon payment:\n$1,000 x 14% / 2 = $70\n\nNext, calculate the number of semiannual periods:\n10 years x 2 = 20 periods\n\nThen, calculate the present value of the coupon payments using the formula:\nPV = C x [1 - (1 + r)^-n] / r\nwhere:\nC = semiannual coupon payment\nr = semiannual interest rate\nn = number of semiannual periods\n\nPV = $70 x [1 - (1 + 0.10 / 2)^-20] / 0.10 / 2\nPV = $70 x [1 - (1.05)^-20] / 0.05\nPV = $70 x [1 - 0.37689] / 0.05\nPV = $70 x 0.62311 / 0.05\nPV = $872.35\n\nFinally, calculate the present value of the bond:\nPV of bond = PV of coupon payments + PV of principal\nPV of bond = $872.35 + $1,000\nPV of bond = $1,872.35\n\nTherefore, the value of bond D is $1,872.35." }, "finish_reason": "STOP" } ], "object": "chat.completion", "created": 1708562069, "usage": { "prompt_tokens": 1140, "completion_tokens": 1288, "total_tokens": 2428 } }