Question 1189743
Here's how to calculate the bond price:

**Understanding the Problem**

The investor wants to earn a 12% annual return (compounded semi-annually) on their investment. The bond pays a 10% annual coupon (paid semi-annually) and has a face value of $50,000, maturing in 25 years. We need to find the present value of this bond's future cash flows, discounted at the investor's desired rate of return.

**Calculations**

1.  **Semi-annual Coupon Payment:**
    *   Annual coupon = 10% * $50,000 = $5,000
    *   Semi-annual coupon = $5,000 / 2 = $2,500

2.  **Semi-annual Discount Rate:**
    *   Annual discount rate = 12%
    *   Semi-annual discount rate = 12% / 2 = 6% = 0.06

3.  **Number of Periods:**
    *   Number of years = 25
    *   Number of semi-annual periods = 25 * 2 = 50

4.  **Present Value of Coupon Payments:**
    We use the present value of an annuity formula:

    PV of coupons = PMT * [1 - (1 + r)^-n] / r

    Where:
    *   PV = Present Value
    *   PMT = Periodic payment ($2,500)
    *   r = Discount rate per period (0.06)
    *   n = Number of periods (50)

    PV of coupons = $2,500 * [1 - (1 + 0.06)^-50] / 0.06
    PV of coupons = $2,500 * [1 - 0.0534] / 0.06
    PV of coupons ≈ $2,500 * 15.77
    PV of coupons ≈ $39,425

5.  **Present Value of Face Value:**
    We discount the face value back to the present:

    PV of face value = FV / (1 + r)^n

    Where:
    *   FV = Face Value ($50,000)
    *   r = Discount rate per period (0.06)
    *   n = Number of periods (50)

    PV of face value = $50,000 / (1 + 0.06)^50
    PV of face value ≈ $50,000 / 18.42
    PV of face value ≈ $2,714

6.  **Bond Price:**
    The bond price is the sum of the present values of the coupon payments and the face value:

    Bond Price = PV of coupons + PV of face value
    Bond Price ≈ $39,425 + $2,714
    Bond Price ≈ $42,139

**Answer:**

The investor should be willing to pay approximately $42,139 for the bond.