A four-year bond has a 7% coupon rate and a face value of $1,000. If the current price of the bond is $904.90, calculate the yield to maturity of the bond (assuming annual interest payments).Group of answer choices9%10%7%5%

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The yield to maturity (YTM) of a bond is the internal rate of return (IRR) if the bond is held until maturity. It's the discount rate that makes the present value of a bond's future cash flows equal to its current market price.

Here are the steps to calculate the YTM:

1. Identify the bond's characteristics:

   • The bond's face value (FV) is $1,000.
   • The bond's annual coupon payment (C) is 7% of the face value, which is $70.
   • The bond's current market price (P) is $904.90.
   • The bond's time to maturity (n) is 4 years.

2. Set up the equation for the present value of the bond's future cash flows, which is the sum of the present value of the annual coupon payments and the present value of the face value:

   P = C * (1 - (1 + r)^-n) / r + FV / (1 + r)^n

   where r is the yield to maturity.

3. Since we don't know the yield to maturity, we can't solve this equation directly. Instead, we need to use a trial-and-error approach or a financial calculator to find the value of r that makes the left side of the equation equal to the right side.

4. Using a financial calculator or Excel's RATE function, we find that the yield to maturity is approximately 10%.

So, the yield to maturity of the bond is 10%.

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To calculate the yield to maturity (YTM) of the bond, we need to solve for the discount rate that makes the present value of the bond's cash flows equal to its current price. The bond's cash flows consist of the annual coupon payments and the face value at maturity.

The formula for the present value of the bond is:

Price = C * (1 - (1 + r)^-n) / r + FV / (1 + r)^n

where C is the annual coupon payment, r is the yield to maturity, n is the number of periods, and FV is the face value of the bond.

In this case, the annual coupon payment is 7% * $1,000 =$70, the number of periods is 4 years, and the face value of the bond is $1,000.

We can set up the equation as follows:

$904.90 =$70 * (1 - (1 + r)^-4) / r + $1,000 / (1 + r)^4

This equation can be solved using a financial calculator or spreadsheet software. By trial and error or using a financial calculator, we find that the yield to maturity that satisfies this equation is approximately 10%.

Therefore, the yield to maturity of the bond is 10%.