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 approximatelyCorrect!  $913.4   $851.4   $888.7   $942.1

To find 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 annual coupon payment. This is the face value of the bond multiplied by the annual coupon rate: $1,000 * 3$30.

Step 2: Calculate the present value of the annual coupon payments. This is the sum of the present values of each individual payment. Since the yield is 5%, we use this as the discount rate. The formula for the present value of an annuity is:

PV = C * [(1 - (1 + r)^-n) / r]

where:

• PV is the present value
• C is the annual coupon payment
• r is the yield
• n is the number of years until maturity

Substituting the given values, we get:

PV = $30 * [(1 - (1 + 5$130.20

Step 3: Calculate the present value of the face value at maturity. This is the face value discounted back to the present using the yield as the discount rate. The formula for the present value of a single sum is:

PV = FV / (1 + r)^n

where:

• PV is the present value
• FV is the face value
• r is the yield
• n is the number of years until maturity

Substituting the given values, we get:

PV = $1,000 / (1 + 5$783.53

Step 4: Add the present values calculated in steps 2 and 3 to get the market price of the bond:

$130.20 +$783.53 = $913.73

So, the market price of the bond is approximately $913.4.