A four-year bond has an 8% coupon rate and a face value of $1,000. If the current price of the bond is $967.60, calculate the yield to maturity of the bond (assume annual coupon payment and annual compounding).

Group of answer choices

9%

10%

7%

5%

The yield to maturity (YTM) of a bond can be found by solving for the discount rate that equates the present value of the bond's future cash flows to its current price. Here's the breakdown of the calculation:

- **Face value of the bond (FV):** $1,000
- **Coupon rate:** 8% annually
- **Coupon payment (C):** $ 8\% \times 1,000 = 80 $
- **Current price of the bond (P):** $967.60
- **Number of years (n):** 4 years

The formula for the bond price is:

\[
P = \sum_{t=1}^{n} \frac{C}{(1 + YTM)^t} + \frac{FV}{(1 + YTM)^n}
\]

Where $ P $ is the current price, $ C $ is the annual coupon payment, $ FV $ is the face value, $ n $ is the number of periods, and $ YTM $ is the yield to maturity.

### Substituting the known values:

\[
967.60 = \frac{80}{(1 + YTM)^1} + \frac{80}{(1 + YTM)^2} + \frac{80}{(1 + YTM)^3} + \frac{80}{(1 + YTM)^4} + \frac{1000}{(1 + YTM)^4}
\]

This equation can be solved iteratively or using a financial calculator. Let's calculate it.

The yield to maturity (YTM) of the bond is approximately **9%**.

Let me know if you need further details or explanations!

Here are 5 related questions you can explore:
1. What factors influence a bond's yield to maturity?
2. How does YTM differ from the coupon rate?
3. What is the relationship between bond price and interest rates?
4. How does YTM impact bond investing decisions?
5. What is the difference between current yield and YTM?

**Tip:** Yield to maturity assumes that all coupon payments are reinvested at the same rate as the YTM.

A four-year bond has an 8% coupon rate and a face value of $1,000. If the current price of the bond is $967.60, calculate the yield to maturity of the bond (assume annual coupon payment and annual compounding).

Learn how to calculate the yield to maturity (YTM) for a 4-year bond with an 8% coupon rate and a face value of $1,000, given a current price of $967.60. This problem involves key financial concepts like bond pricing and discounting future cash flows.

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