Input
Output
Evaluation Input Image

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: 1,000x141,000 x 14% / 2 = 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 = 70x[1(1+0.10/2)20]/0.10/2PV=70 x [1 - (1 + 0.10 / 2)^-20] / 0.10 / 2 PV = 70 x [1 - (1.05)^-20] / 0.05 PV = 70x[10.37689]/0.05PV=70 x [1 - 0.37689] / 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 = 872.35+872.35 + 1,000 PV of bond = $1,872.35

Therefore, the value of bond D is $1,872.35.


Difficulty: Medium

Subfield: Managerial Finance

Evaluation

Evaluation ID
ef1af955-d8a1-4aa7-bb2e-d4d763496ee9
Created
February 21, 2024
Raw Output
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        "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."
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