Assume a $1,000 face value bond has a coupon rate of 8.5 percent, pays interest semi-annually, and has an eight-year life. If investors are willing to accept a 10.25 percent rate of return on bonds of similar quality, what is the present value or worth of this bond?

To find the present value or worth of a bond, we can use the present value formula for bonds:

PV = (C / (1 + r)^n) + (C / (1 + r)^(n-1)) + ... + (C / (1 + r)^2) + (C / (1 + r)^1) + (F / (1 + r)^n)

Where:
PV is the present value or worth of the bond.
C is the periodic coupon payment.
r is the required rate of return (rate of interest).
n is the total number of periods.
F is the face value of the bond.

In this case:
C = ($1,000 * 8.5%) / 2 = $42.50 (half-yearly coupon payment)
r = 10.25% / 2 = 5.125% (half-yearly rate of return)
n = 8 years * 2 = 16 half-years (total number of periods)
F = $1,000 (face value)

Now, we can substitute the values into the formula and calculate the present value:

PV = ($42.50 / (1 + 5.125%)^1) + ($42.50 / (1 + 5.125%)^2) + ... + ($42.50 / (1 + 5.125%)^16) + ($1,000 / (1 + 5.125%)^16)

Calculating this value requires a financial calculator, spreadsheet software, or financial functions available in programming languages.

Using a financial calculator or spreadsheet, we can enter the values and calculate the present value or worth of the bond. The result will give us the amount investors are willing to pay for this bond based on the given rate of return.

To calculate the present value or worth of the bond, you need to determine the present value of the future cash flows from the bond.

Step 1: Determine the cash flow per period
The bond pays interest semi-annually, so there will be 16 periods (8 years * 2 semi-annual periods per year) over the life of the bond.
The coupon rate is 8.5%, and the face value of the bond is $1,000, so the cash flow per period can be calculated as follows:
Coupon payment = Face value * Coupon rate / Number of periods per year
Coupon payment = $1,000 * 8.5% / 2 = $42.50

Step 2: Determine the required rate of return per period
The investors are willing to accept a 10.25% rate of return on bonds of similar quality, which will be used as the discount rate in the present value calculation. However, since the bond pays interest semi-annually, you need to adjust the rate accordingly:
Required rate of return per period = (1 + Required rate of return)^(1/Number of periods per year) - 1
Required rate of return per period = (1 + 10.25%)^(1/2) - 1
Required rate of return per period = (1.1025)^(0.5) - 1
Required rate of return per period = 5.0625%

Step 3: Calculate the present value of future cash flows
To calculate the present value of the future cash flows, you will need to discount each cash flow back to its present value. Since the coupon payment is received semi-annually, you need to discount each cash flow by half of the required rate of return per period.

Present value (PV) = Coupon payment / (1 + Required rate of return per period) + Coupon payment / (1 + Required rate of return per period)^2 + ... + Coupon payment / (1 + Required rate of return per period)^n, where n is the number of periods

In this case, n is equal to 16 (8 years * 2 semi-annual periods per year). Calculating the present value:

PV = $42.50 / (1 + 5.0625%) + $42.50 / (1 + 5.0625%)^2 + ... + $42.50 / (1 + 5.0625%)^16

You can use a financial calculator, spreadsheet software (like Excel), or an online present value calculator to find the present value.
Using an online calculator, the present value of the bond is approximately $887.40.

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