document.write( "Question 1189743: How much should an investor be willing to pay now for 10%, 50, 000 bond that will mature in 25 years and pays interest semi-annually, if it wants to make 12% nominal interest compounded semi-annually on a bond
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Algebra.Com's Answer #849266 by CPhill(1959)\"\" \"About 
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Here's how to calculate the bond price:\r
\n" ); document.write( "\n" ); document.write( "**Understanding the Problem**\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "**Calculations**\r
\n" ); document.write( "\n" ); document.write( "1. **Semi-annual Coupon Payment:**
\n" ); document.write( " * Annual coupon = 10% * $50,000 = $5,000
\n" ); document.write( " * Semi-annual coupon = $5,000 / 2 = $2,500\r
\n" ); document.write( "\n" ); document.write( "2. **Semi-annual Discount Rate:**
\n" ); document.write( " * Annual discount rate = 12%
\n" ); document.write( " * Semi-annual discount rate = 12% / 2 = 6% = 0.06\r
\n" ); document.write( "\n" ); document.write( "3. **Number of Periods:**
\n" ); document.write( " * Number of years = 25
\n" ); document.write( " * Number of semi-annual periods = 25 * 2 = 50\r
\n" ); document.write( "\n" ); document.write( "4. **Present Value of Coupon Payments:**
\n" ); document.write( " We use the present value of an annuity formula:\r
\n" ); document.write( "\n" ); document.write( " PV of coupons = PMT * [1 - (1 + r)^-n] / r\r
\n" ); document.write( "\n" ); document.write( " Where:
\n" ); document.write( " * PV = Present Value
\n" ); document.write( " * PMT = Periodic payment ($2,500)
\n" ); document.write( " * r = Discount rate per period (0.06)
\n" ); document.write( " * n = Number of periods (50)\r
\n" ); document.write( "\n" ); document.write( " PV of coupons = $2,500 * [1 - (1 + 0.06)^-50] / 0.06
\n" ); document.write( " PV of coupons = $2,500 * [1 - 0.0534] / 0.06
\n" ); document.write( " PV of coupons ≈ $2,500 * 15.77
\n" ); document.write( " PV of coupons ≈ $39,425\r
\n" ); document.write( "\n" ); document.write( "5. **Present Value of Face Value:**
\n" ); document.write( " We discount the face value back to the present:\r
\n" ); document.write( "\n" ); document.write( " PV of face value = FV / (1 + r)^n\r
\n" ); document.write( "\n" ); document.write( " Where:
\n" ); document.write( " * FV = Face Value ($50,000)
\n" ); document.write( " * r = Discount rate per period (0.06)
\n" ); document.write( " * n = Number of periods (50)\r
\n" ); document.write( "\n" ); document.write( " PV of face value = $50,000 / (1 + 0.06)^50
\n" ); document.write( " PV of face value ≈ $50,000 / 18.42
\n" ); document.write( " PV of face value ≈ $2,714\r
\n" ); document.write( "\n" ); document.write( "6. **Bond Price:**
\n" ); document.write( " The bond price is the sum of the present values of the coupon payments and the face value:\r
\n" ); document.write( "\n" ); document.write( " Bond Price = PV of coupons + PV of face value
\n" ); document.write( " Bond Price ≈ $39,425 + $2,714
\n" ); document.write( " Bond Price ≈ $42,139\r
\n" ); document.write( "\n" ); document.write( "**Answer:**\r
\n" ); document.write( "\n" ); document.write( "The investor should be willing to pay approximately $42,139 for the bond.
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