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There is a bond that has a quoted price of 106.818 and a par value of $2,000. The coupon rate is 7.11 percent and the bond matures in 17 years. If the bond makes semiannual coupon payments, what is the YTM of the bond

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User Roald
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1 Answer

2 votes

Final answer:

The Yield to Maturity (YTM) of a bond with semiannual coupon payments can be calculated using the YTM formula. In this case, the YTM is approximately 3.96%.

Step-by-step explanation:

The Yield to Maturity (YTM) of a bond refers to the total return an investor would receive if they held the bond until it matures. To calculate YTM for a bond with semiannual coupon payments, you need to use financial formulas and equations.



First, we need to calculate the semiannual coupon payment. This can be done by multiplying the coupon rate by the par value and dividing by 2, since the bond makes semiannual coupon payments. So, the semiannual coupon payment is $2,000 * 7.11% / 2 = $71.10.



Next, we can use the YTM formula to calculate the yield. The formula is:



YTM = (C + (F - P) / n) / ((F + P) / 2)



where C is the coupon payment, F is the par value, P is the quoted price, and n is the number of periods. In this case, C = $71.10, F = $2,000, P = $106.818, and n = 17 * 2 = 34 (since there are 34 semiannual periods in 17 years).



Plugging in the values, we get:



YTM = ($71.10 + ($2,000 - $106.818) / 34) / (($2,000 + $106.818) / 2) = 0.0395574, or 3.96% (rounded to two decimal places).

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