To solve this, we’ll break it into the three parts:

a. Current Yield

The current yield of a bond is calculated as: $\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Market Price}}$

• Coupon Rate: $8.39\%$
• Par Value: $1,000$
• Market Price: $1,020.56$

The annual coupon payment is: $\text{Coupon Payment} = \text{Coupon Rate} \times \text{Par Value} = 0.0839 \times 1,000 = 83.90$

Thus: $\text{Current Yield} = \frac{83.90}{1,020.56} \approx 8.22\%$

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b. Approximate Yield to Maturity (YTM)

The approximate YTM can be estimated using this formula: $\text{Approximate YTM} = \frac{\text{Coupon Payment} + \frac{\text{Par Value} - \text{Price}}{\text{Years to Maturity}}}{\frac{\text{Par Value} + \text{Price}}{2}}$

• Coupon Payment: $83.90$
• Par Value: $1,000$
• Market Price: $1,020.56$
• Years to Maturity: $9$

Substituting the values: $\text{Approximate YTM} = \frac{83.90 + \frac{1,000 - 1,020.56}{9}}{\frac{1,000 + 1,020.56}{2}}$

First, calculate: $\frac{1,000 - 1,020.56}{9} = -2.29$ $\frac{1,000 + 1,020.56}{2} = 1,010.28$

Now: $\text{Approximate YTM} = \frac{83.90 - 2.29}{1,010.28} \approx \frac{81.61}{1,010.28} \approx 8.08\%$

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c. Yield to Maturity Using a Financial Calculator

To find the precise YTM using a financial calculator, we use the bond's time value of money (TVM) inputs:

• $N$: $9$ years (number of periods)
• $PV$: $-1,020.56$ (present value, the negative sign reflects cash outflow)
• $PMT$: $83.90$ (annual coupon payment)
• $FV$: $1,000$ (future value, par value)

Using a financial calculator or software, solve for $I/Y$ (YTM). This yields approximately:

$\text{YTM} \approx 8.05\%$

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Final Results:

• a. Current Yield: $8.22\%$
• b. Approximate YTM: $8.08\%$
• c. Precise YTM: $8.05\%$

Would you like further details or help setting up a financial calculator?

Expanding Questions:

1. How does the YTM differ from the current yield in terms of calculation and meaning?
2. How would the bond's price change if market interest rates rose to 9%?
3. What happens to YTM if the bond is callable before maturity?
4. How can bond duration help assess interest rate risk for this bond?
5. What are the tax implications of receiving bond interest and capital gains?

Tip:

Always compare the YTM to market interest rates to assess whether the bond is over- or under-valued relative to other opportunities.