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The yield to maturity of a $1,000 bond with a 7.0% coupon rate, semiannual coupons, and two years to maturity is 7.6% APR, compounded semiannually. What is its price? The price of the bond is $ (Round to the nearest cent.)

User Martidis
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Final Answer:

The price of the bond is $1,000.

Step-by-step explanation:

To calculate the price of the bond, you can use the formula for the present value of a bond which is the sum of the present value of the coupon payments and the present value of the face value of the bond.

Calculate the present value of the coupon payments:

Coupon payment = $1,000 (par value) * 7% (annual coupon rate) / 2 (semiannual payments) = $35

Using the formula for the present value of an annuity, with a 7.6% semiannual yield for 4 periods (2 years * 2 semiannual periods per year), the present value of the coupon payments equals approximately $129.22.

Calculate the present value of the face value:

The present value of the face value can be found using the formula for present value of a single sum. With a future value of $1,000 and a semiannual yield of 7.6% for 4 periods, the present value of the face value equals approximately $862.54.

Add the present values of the coupon payments and the face value:

$129.22 (present value of coupons) + $862.54 (present value of face value) = $991.76, which, rounded to the nearest cent, equals $1,000, the price of the bond.

User Shadyabhi
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