What is the current price of a $1,000, 5% coupon bond that pays interest semi-annually if the bond matures in ten years and has a yield-to-maturity of 7.5%?

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Quizplus · Accepted Answer

The price of a bond can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the face value of the bond). The coupon payment is $1,000 * 5% = $50 annually, or $25 semi-annually. With a yield of 7.5% annually, or 3.75% semi-annually, over 20 periods (10 years semi-annually), the calculation is as follows: Price = ($25 / 0.0375) * (1 - (1 / (1 + 0.0375)^20)) + $1,000 / (1 + 0.0375)^20, which approximates to $826.30.

What Is the Current Price of a $1,000, 5% Coupon