Let's solve the problem from the image step-by-step.

Problem Breakdown

1. Yield to Maturity (YTM)

• Given Information:

  • Par Value ($FV$): $1,000
  • Coupon Rate: 6% annual, which means the coupon payment is $0.06 \times 1,000 = 60$ dollars per year.
  • Current Price ($P_0$): $943
  • Maturity: 12 years

  The Yield to Maturity (YTM) is the interest rate that equates the present value of all future cash flows (coupon payments and face value at maturity) to the bond's current price.

  The formula for YTM is: $P_0 = \sum_{t=1}^{n} \frac{C}{(1 + YTM)^t} + \frac{FV}{(1 + YTM)^n}$ Where:

  • $P_0$ is the current price ($943)
  • $C$ is the annual coupon payment ($60)
  • $FV$ is the face value of the bond ($1,000)
  • $n$ is the number of years to maturity (12 years)
  • $YTM$ is the yield to maturity (what we are solving for)

Since this equation involves solving for $YTM$, it's often solved iteratively or using a financial calculator.

2. Price of the bond in 4 years

• Assuming the YTM remains constant, the bond will have 8 years to maturity after 4 years. You can then recalculate the bond price using the YTM calculated above.

Let me calculate the YTM first, then proceed to calculate the bond price in 4 years.

I'll start with the YTM calculation using an iterative approach.The yield to maturity (YTM) for the bond is approximately 6.71%.

Next Step:

Now, let's calculate the price of the bond in 4 years, assuming the YTM remains constant at 6.71%. After 4 years, there will be 8 years remaining to maturity. I'll use the same bond pricing formula with 8 years left. Let me calculate that.The price of the bond in 4 years, assuming the yield to maturity remains constant at 6.71%, will be approximately $957.33.

Summary:

1. Yield to Maturity (YTM): 6.71%
2. Price of the bond in 4 years: $957.33

Would you like more details on the calculations?

Here are 5 related questions to deepen understanding:

1. How would the bond price change if interest rates rise above the YTM?
2. What impact does a shorter time to maturity have on bond price volatility?
3. How is the coupon rate different from the yield to maturity?
4. What is the relationship between bond price and YTM?
5. How can we estimate bond price changes without using a financial calculator?

Tip: The YTM is the discount rate at which the bond's future cash flows equal its current price. It serves as an essential metric for comparing bonds.