  A​ bond's market price is 

​$750750. 

 It has a 

​$1 comma 0001,000 

par​ value, will mature in 

66 

​years, and has a coupon interest rate of 

1212 

percent annual​ interest, but makes its interest payments semiannually.  What is the​ bond's yield to​ maturity?  What happens to the​ bond's yield to maturity if the bond matures in 

1212 

​years?  What if it matures in 

33 

​years?

To find the bond's yield to maturity (YTM), we'll need to solve the following equation, which equates the bond's current price to the present value of its future cash flows:

\[
P = \sum \left( \frac{C}{(1 + r/2)^{2t}} \right) + \frac{\text{Par Value}}{(1 + r/2)^{2N}}
\]

Where:
- $ P $ is the bond's market price
- $ C $ is the semiannual coupon payment
- $ r $ is the annual yield to maturity (YTM) we're solving for
- $ t $ is the period number (from 1 to $ N $)
- $ N $ is the number of years to maturity

Given Data:
- Market price $ P = \$750 $
- Par value $ = \$1,000 $
- Annual coupon rate $ = 12\% $
- Coupon payment $ = 12\% \times 1,000 / 2 = \$60 $ per semiannual period

We'll need to solve for $ r $ using iterative methods, as there is no closed-form solution for YTM. We'll calculate the YTM for three different maturities:

1. **Maturity of 6 years** (12 semiannual periods)
2. **Maturity of 12 years** (24 semiannual periods)
3. **Maturity of 3 years** (6 semiannual periods)

Let's calculate the YTM for each scenario.

Learn how to calculate the bond's yield to maturity (YTM) for different maturity periods. Understand the impact of maturity length on YTM with detailed calculations based on a bond priced at $750, with a $1,000 par value and a 12% coupon rate. Suitable for advanced high school students studying finance and investments.

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