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A European government bond maturing in 6 years has a fixed coupon rate of 4% pa, paid annually.The bond's yield-to-maturity (YTM) is currently 4% pa, given as an annualised percentage rate (APR) compounding annually.The face value of the bond is $100. Calculate the bond price. All answer options below are rounded to 6 decimal points.Question 2Select one:a.$79.031453b.$94.665404c.$100d.$124e.$126.53190

Question

A European government bond maturing in 6 years has a fixed coupon rate of 4% pa, paid annually.The bond's yield-to-maturity (YTM) is currently 4% pa, given as an annualised percentage rate (APR) compounding annually.The face value of the bond is 100.Calculatethebondprice.Allansweroptionsbelowareroundedto6decimalpoints.Question2Selectone:a.100. Calculate the bond price. All answer options below are rounded to 6 decimal points.Question 2Select one:a.79.031453b.94.665404c.94.665404c.100d.124e.124e.126.53190

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Solution

The price of a bond is calculated by summing the present value of its future cash flows, which includes the present value of its future coupon payments and the present value of its face value.

Given that the bond has a fixed coupon rate of 4% per annum, paid annually, the annual coupon payment is 4% of the face value of 100,whichis100, which is 4.

The yield-to-maturity (YTM) is currently 4% per annum, which is used as the discount rate.

The bond is maturing in 6 years, so there will be 6 coupon payments of 4eachandafacevalueof4 each and a face value of 100 to be paid at the end of 6 years.

The present value of the future coupon payments is calculated as follows:

PV_Coupon = 4/(1+0.04)+4/(1+0.04) + 4/(1+0.04)^2 + 4/(1+0.04)3+4/(1+0.04)^3 + 4/(1+0.04)^4 + 4/(1+0.04)5+4/(1+0.04)^5 + 4/(1+0.04)^6 = $21.8494

The present value of the face value is calculated as follows:

PV_Face Value = 100/(1+0.04)6=100/(1+0.04)^6 = 79.3721

Therefore, the price of the bond is the sum of the present value of the future coupon payments and the present value of the face value, which is 21.8494+21.8494 + 79.3721 = $101.2215

So, the closest answer to the calculated bond price is option c. $100.

This problem has been solved

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