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A European government bond maturing in 1 year has a fixed coupon rate of 4.5% pa, paid annually.The bond's yield-to-maturity (YTM) is currently 2% 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.$104.5b.$102.45098c.$97.607656d.$94.280336e.$4.411765

Question

A European government bond maturing in 1 year has a fixed coupon rate of 4.5% pa, paid annually.The bond's yield-to-maturity (YTM) is currently 2% 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.104.5b.102.45098c.102.45098c.97.607656d.94.280336e.94.280336e.4.411765

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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 face value and the present value of its coupon payments.

Here, the face value of the bond is $100, the coupon rate is 4.5% per annum, and the yield to maturity (YTM) is 2% per annum.

Step 1: Calculate the present value of the face value, which is the face value divided by (1 + YTM) to the power of the number of years to maturity.

PV of Face Value = Face Value / (1 + YTM) ^ n = 100/(1+0.02)1=100 / (1 + 0.02) ^ 1 = 100 / 1.02 = $98.03921569

Step 2: Calculate the present value of the coupon payments, which is the annual coupon payment divided by (1 + YTM) to the power of the number of years to maturity.

PV of Coupon Payments = Annual Coupon Payment / (1 + YTM) ^ n = (100∗0.045)/(1+0.02)1=100 * 0.045) / (1 + 0.02) ^ 1 = 4.411764705 / 1.02 = $4.324674556

Step 3: Add the present value of the face value and the present value of the coupon payments to get the bond price.

Bond Price = PV of Face Value + PV of Coupon Payments = 98.03921569+98.03921569 + 4.324674556 = $102.363890246

So, the closest answer to the bond price is option b. $102.45098.

This problem has been solved

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