You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2022. All of the bonds have a par value of $1,000 and pay semiannual coupons.

RateMaturity Month/YearBidAskedChangeAsk Yield

??question mark

May 33

103.4755

103.5483

+.3158

6.219

5.774

May 36

104.5095

104.6552

+.4425

??

6.218

May 42

??question mark

??question mark

+.5548

4.251

In the above table, find the Treasury bond that matures in May 2036. What is your yield to maturity if you buy this bond?

**Note**

To find the yield to maturity (YTM) for the Treasury bond maturing in May 2036, we can use the given information and the current market prices. Here's a breakdown of how to calculate it:

### Bond Details

- **Current Year:** 2022
- **Maturity Year:** 2036
- **Years to Maturity:** $2036 - 2022 = 14$ years
- **Bid Price:** 104.5095% of par
- **Asked Price:** 104.6552% of par
- **Coupon Rate:** Not provided (let’s assume it’s the same as Ask Yield for calculation)
- **Ask Yield:** 6.218%

### Calculating YTM

YTM can be calculated using the bond's coupon payments, current price, face value, and years to maturity. The formula is:

\[
\text{Price} = \sum_{t=1}^{N} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^N}
\]

Where:
- $ C $ = semiannual coupon payment
- $ r $ = semiannual YTM
- $ F $ = face value of the bond
- $ N $ = total number of periods (28 semiannual periods)

#### Steps:

1. **Convert Ask Price to Dollar Amount:**
   \[
   \text{Ask Price} = \frac{104.6552}{100} \times 1,000 = 1,046.552
   \]

2. **Approximate YTM using Ask Yield:**
   - Use the given Ask Yield as the annual YTM to estimate the coupon rate:
   - Annual YTM ≈ 6.218%

3. **Calculate Semiannual Coupon Payment:**
   - If $ \text{Annual Coupon Rate} = 6.218\% $, then
   \[
   C = \frac{6.218\% \times 1,000}{2} = 31.09
   \]

4. **Calculate Semiannual YTM:**
   - Given Ask Yield (annual), convert to semiannual:
   \[
   \text{Semiannual YTM} = \frac{6.218}{2} = 3.109\%
   \]

### Conclusion

- **Your yield to maturity if you buy this bond at the ask price is approximately 6.218% annually.**

If you'd like further clarification or more calculations, let me know!

---

**Need help with details? Feel free to ask!**

1. How is YTM different from coupon rate?
2. How do changes in price affect yield?
3. Why use semiannual payments in calculations?
4. How does market interest rate affect bond prices?
5. What other factors impact YTM?

**Tip:** Always check whether the bond’s price is given as a percentage of par to avoid calculation errors.

Learn how to calculate the yield to maturity (YTM) for a Treasury bond maturing in May 2036. Understand the bond valuation process and the formula for YTM. Includes step-by-step calculations based on current market prices and semiannual coupons.

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