Question

Consider an 8% coupon bond selling for $953.10 with three years until maturity making annual coupon payments. The interest rates in the next three years will be, with certainty,

r1 = 8%, r2 = 10%, and r3 = 12%. Calculate the yield to maturity and realized compound yield of the bond.

Answer 1

9.88 and 9.98

Answer 2

$903.59

Answer 3

100

Answer 4

12%

Answer 5

please give me answer

Answer 6

[AI-generated answer — Explain Bot]

To calculate the yield to maturity (YTM) and realized compound yield of the bond, we need to follow these steps:

Step 1: Determine the annual coupon payment.
The coupon payment can be calculated by multiplying the coupon rate (8%) with the face value of the bond.
Coupon payment = Coupon rate * Face value
Coupon payment = 8% * Face value

Step 2: Determine the present value of the coupon payments.
To calculate the present value of the coupon payments, we will discount each coupon payment by the corresponding interest rate.
Present value of the coupon payments = (Coupon payment / (1 + interest rate))^n
Where n represents the number of years until maturity.

Step 3: Determine the present value of the face value.
The present value of the face value can be calculated by dividing the current price of the bond (selling price) by (1 + interest rate)^n.

Step 4: Calculate the total present value of the bond.
The total present value of the bond is the sum of the present values of the coupon payments and the present value of the face value.

Step 5: Use trial and error to find the yield to maturity.
Now that we have all the necessary values, we can use trial and error to find the yield to maturity that satisfies the equation:
Total present value of the bond = Current selling price

Step 6: Calculate the realized compound yield.
The realized compound yield can be calculated using the following formula:
Realized compound yield = (1 + YTM)^(1/n) - 1

Using these steps, let's calculate the yield to maturity and the realized compound yield of the bond:

Step 1: Determine the annual coupon payment.
Coupon payment = 8% * Face value

Step 2: Determine the present value of the coupon payments.
Present value of the coupon payments = (Coupon payment / (1 + interest rate))^n

Present value of the coupon payment for the first year = (Coupon payment / (1 + r1))^1
Present value of the coupon payment for the second year = (Coupon payment / (1 + r2))^2
Present value of the coupon payment for the third year = (Coupon payment / (1 + r3))^3

Step 3: Determine the present value of the face value.
Present value of the face value = Current selling price / (1 + interest rate)^n

Step 4: Calculate the total present value of the bond.
Total present value of the bond = Present value of the coupon payments + Present value of the face value

Step 5: Use trial and error to find the yield to maturity.
Start with an initial guess for the yield to maturity (YTM) and calculate the total present value of the bond using the formula from Step 4. Adjust the YTM until the total present value of the bond is equal to the current selling price.

Step 6: Calculate the realized compound yield.
Realized compound yield = (1 + YTM)^(1/n) - 1

By following these steps, you should be able to calculate the yield to maturity and the realized compound yield of the bond.