Consider a 5-year bond with a face value of $1,000 and an annual coupon rate of 3%. If the yield is 5% then the market price of this bond will be approximately

To calculate the market price of the bond, we need to calculate the present value of the bond's future cash flows, which include the annual coupon payments and the face value at maturity.

Step 1: Calculate the present value of the coupon payments.

The bond pays an annual coupon of 3% of the face value, which is $1,000 * 0.03 =$30.

The present value of these payments is calculated as an annuity. The formula for the present value of an annuity is:

PVA = PMT * [(1 - (1 + r)^-n) / r]

where: PMT = annual payment = $30 r = yield = 5% = 0.05 n = number of years = 5

So, the present value of the coupon payments is:

PVA = $30 * [(1 - (1 + 0.05)^-5) / 0.05] =$30 * 4.3295 = $129.89

Step 2: Calculate the present value of the face value.

The face value is received at the end of the bond's life, so it's a single future payment. The formula for the present value of a single future payment is:

PV = FV / (1 + r)^n

where: FV = face value = $1,000 r = yield = 5% = 0.05 n = number of years = 5

So, the present value of the face value is:

PV = $1,000 / (1 + 0.05)^5 =$1,000 / 1.2763 = $783.53

Step 3: Add the present values to get the market price of the bond.

The market price of the bond is the sum of the present values of the coupon payments and the face value:

Market price = PVA + PV = $129.89 +$783.53 = $913.42

So, the market price of the bond is approximately $913.42.