Final answer:
To determine the realized yield of the bond, we calculate the total return by adding the interest payments and capital gains. The annual coupon payment and capital gains are calculated based on the bond's purchase and selling prices. The realized yield is then determined by dividing the total return by the purchase price and converting the result to a percentage.
Step-by-step explanation:
To calculate the realized yield of the bond, we need to determine the total return, which includes both interest payments and capital gains. First, let's calculate the interest payments. The bond pays a coupon of 13% semiannually, so the annual coupon is 26% (13% x 2). The annual coupon payment is calculated by multiplying the face value of the bond ($1,000) by the annual coupon rate, which equals $260. Since Rachel bought the bond six years ago, she would have received 12 coupon payments of $260, totaling $3,120 ($260 x 12).
Next, let's calculate the capital gains. Rachel bought the bond for $985.21 and today it is priced at $998.35. The capital gain is the difference between the purchase price and the selling price, which equals $13.14 ($998.35 - $985.21).
The total return is calculated by adding the interest payments and capital gains: $3,120 + $13.14 = $3,133.14.
To determine the realized yield, we divide the total return by the purchase price and convert the result to a percentage: ($3,133.14 / $985.21) * 100% = 317.844%, which we can round to 318%. Therefore, Rachel's realized yield would be approximately 318%.