To calculate the current price of the bond, we need to calculate the present value of the bond's cash flows, which are the semi-annual coupon payments and the face value payment at maturity.

Step 1: Calculate the semi-annual coupon payment
The bond pays a 6.9% coupon rate semi-annually, so the semi-annual coupon payment is $1000 * 6.9% / 2 = $34.5.

Step 2: Calculate the semi-annual yield
The bond is currently yielding 8.1% in the market, so the semi-annual yield is 8.1% / 2 = 4.05%.

Step 3: Calculate the present value of the coupon payments
The bond will make 3 * 2 = 6 coupon payments over its remaining life. The present value of these payments is $34.5 / (1 + 4.05%) + $34.5 / (1 + 4.05%)^2 + ... + $34.5 / (1 + 4.05%)^6 = $185.24.

Step 4: Calculate the present value of the face value
The bond will pay its $1000 face value at maturity, so the present value of this payment is $1000 / (1 + 4.05%)^6 = $837.48.

Step 5: Add the present values to find the current price of the bond
The current price of the bond is the sum of the present values of its cash flows, so the current price is $185.24 + $837.48 = $1022.72.

Question

To calculate the current price of the bond, we need to calculate the present value of the bond's cash flows, which are the semi-annual coupon payments and the face value payment at maturity.

Step 1: Calculate the semi-annual coupon payment
The bond pays a 6.9% coupon rate semi-annually, so the semi-annual coupon payment is $1000 * 6.9% / 2 = $34.5.

Step 2: Calculate the semi-annual yield
The bond is currently yielding 8.1% in the market, so the semi-annual yield is 8.1% / 2 = 4.05%.

Step 3: Calculate the present value of the coupon payments
The bond will make 3 * 2 = 6 coupon payments over its remaining life. The present value of these payments is $34.5 / (1 + 4.05%) + $34.5 / (1 + 4.05%)^2 + ... + $34.5 / (1 + 4.05%)^6 = $185.24.

Step 4: Calculate the present value of the face value
The bond will pay its $1000 face value at maturity, so the present value of this payment is $1000 / (1 + 4.05%)^6 = $837.48.

Step 5: Add the present values to find the current price of the bond
The current price of the bond is the sum of the present values of its cash flows, so the current price is $185.24 + $837.48 = $1022.72.

Knowee AI · Accepted Answer

To calculate the current price of the bond, we need to calculate the present value of the bond's cash flows, which are the semi-annual coupon payments and the face value payment at maturity.

Step 1: Calculate the semi-annual coupon payment
The bond pays a 6.9% coupon rate semi-annually, so the semi-annual coupon payment is $1000 * 6.9% / 2 = $34.5.

Step 2: Calculate the semi-annual yield
The bond is currently yielding 8.1% in the market, so the semi-annual yield is 8.1% / 2 = 4.05%.

Step 3: Calculate the present value of the coupon payments
The bond will make 3 * 2 = 6 coupon payments over its remaining life. The present value of these payments is $34.5 / (1 + 4.05%) + $34.5 / (1 + 4.05%)^2 + ... + $34.5 / (1 + 4.05%)^6 = $185.24.

Step 4: Calculate the present value of the face value
The bond will pay its $1000 face value at maturity, so the present value of this payment is $1000 / (1 + 4.05%)^6 = $837.48.

Step 5: Add the present values to find the current price of the bond
The current price of the bond is the sum of the present values of its cash flows, so the current price is $185.24 + $837.48 = $1022.72.

A $1000 face value bond, with a 6.9% coupon rate paid semi-annually and maturing in three years, is currently yielding 8.1% in the market. What is the current price of the bond?

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