To calculate the market price of a 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.

Here are the steps:

1. Calculate the annual coupon payment: This is the face value of the bond multiplied by the annual coupon rate. In this case, it's $1,000 * 3% = $30.

2. Calculate the present value of the annual coupon payments: This is the sum of the present values of each annual coupon payment. Since the yield is 5%, we discount each annual payment by this rate. The formula for the present value of an annuity is C * [(1 - (1 + r)^-n) / r], where C is the annual payment, r is the yield, and n is the number of years. In this case, it's $30 * [(1 - (1 + 5%)^-5) / 5%] = $130.20.

3. Calculate the present value of the face value: This is the face value discounted by the yield rate for the number of years until maturity. The formula for the present value of a single sum is FV / (1 + r)^n, where FV is the face value, r is the yield, and n is the number of years. In this case, it's $1,000 / (1 + 5%)^5 = $783.53.

4. Add the present value of the annual coupon payments to the present value of the face value to get the market price of the bond. In this case, it's $130.20 + $783.53 = $913.73.

So, the market price of this bond will be approximately $913.73. The closest answer choice is $913.4.

Question

To calculate the market price of a 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.

Here are the steps:

1. Calculate the annual coupon payment: This is the face value of the bond multiplied by the annual coupon rate. In this case, it's $1,000 * 3% = $30.

2. Calculate the present value of the annual coupon payments: This is the sum of the present values of each annual coupon payment. Since the yield is 5%, we discount each annual payment by this rate. The formula for the present value of an annuity is C * [(1 - (1 + r)^-n) / r], where C is the annual payment, r is the yield, and n is the number of years. In this case, it's $30 * [(1 - (1 + 5%)^-5) / 5%] = $130.20.

3. Calculate the present value of the face value: This is the face value discounted by the yield rate for the number of years until maturity. The formula for the present value of a single sum is FV / (1 + r)^n, where FV is the face value, r is the yield, and n is the number of years. In this case, it's $1,000 / (1 + 5%)^5 = $783.53.

4. Add the present value of the annual coupon payments to the present value of the face value to get the market price of the bond. In this case, it's $130.20 + $783.53 = $913.73.

So, the market price of this bond will be approximately $913.73. The closest answer choice is $913.4.

Knowee AI · Accepted Answer

To calculate the market price of a 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.

Here are the steps:

1. Calculate the annual coupon payment: This is the face value of the bond multiplied by the annual coupon rate. In this case, it's $1,000 * 3% = $30.

2. Calculate the present value of the annual coupon payments: This is the sum of the present values of each annual coupon payment. Since the yield is 5%, we discount each annual payment by this rate. The formula for the present value of an annuity is C * [(1 - (1 + r)^-n) / r], where C is the annual payment, r is the yield, and n is the number of years. In this case, it's $30 * [(1 - (1 + 5%)^-5) / 5%] = $130.20.

3. Calculate the present value of the face value: This is the face value discounted by the yield rate for the number of years until maturity. The formula for the present value of a single sum is FV / (1 + r)^n, where FV is the face value, r is the yield, and n is the number of years. In this case, it's $1,000 / (1 + 5%)^5 = $783.53.

4. Add the present value of the annual coupon payments to the present value of the face value to get the market price of the bond. In this case, it's $130.20 + $783.53 = $913.73.

So, the market price of this bond will be approximately $913.73. The closest answer choice is $913.4.

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 approximatelyGroup of answer choices$888.7$942.1$851.4$913.4

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