Let's solve each part of this question in detail.
### Part a: Yield to Maturity (YTM)
The yield to maturity (YTM) of a bond can be calculated using the formula:
[tex]\[ \text{YTM} \% = \left( \frac{\text{Face Value} - \text{Current Price}}{\text{Current Price}} \right) \times 100 \][/tex]
In this problem, we have:
- Face Value (FV) = \[tex]$2000
- Current Price (CP) = \$[/tex]824
Using the formula, we plug in the given values:
[tex]\[ \text{YTM} \% = \left( \frac{2000 - 824}{824} \right) \times 100 \][/tex]
First, calculate the numerator:
[tex]\[ 2000 - 824 = 1176 \][/tex]
Next, divide by the current price:
[tex]\[ \frac{1176}{824} \approx 1.4272 \][/tex]
Finally, convert to a percentage:
[tex]\[ 1.4272 \times 100 \approx 142.72 \% \][/tex]
So, the yield to maturity of the bond is approximately 142.72% when rounded to two decimal places.
### Part b: Current Yield
To calculate the current yield, you typically need to know the annual coupon payment of the bond. Since this information is not provided in the problem, the current yield cannot be determined with the given data.
### Summary
Based on the given data, we have:
1. Yield to maturity: 142.72%
2. Current yield: Cannot be determined (more information needed).
