Answer:
The yield to maturity (YTM) of a bond is the internal rate of return (IRR) on the bond, considering its current price, face value, maturity, and the periodic interest payments.
For a zero-coupon bond, the yield to maturity can be calculated using the following formula:
\[ YTM = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1 \]
where:
- \( FV \) is the face value of the bond,
- \( PV \) is the current price of the bond,
- \( n \) is the number of years to maturity.
In this case:
- \( FV = $100 \),
- \( PV = $74.55 \),
- \( n = 5 \) years.
Substitute these values into the formula to calculate the yield to maturity (\( YTM \)).
The yield to maturity (\(YTM\)) for a 5-year zero-coupon, $100 face value bond currently priced at $74.55 is approximately 6.5%.