Final answer:
To calculate the yield to maturity on a 3-year, $1,000 discount bond with a current price of $921, subtract the purchase price from the face value to find the capital gain, divide by the purchase price, and find the annualized rate. The approximate yield to maturity is 2.8% when rounded to one decimal place.
Step-by-step explanation:
The question is asking how to calculate the yield to maturity on a 3-year, $1,000 discount bond with a current price of $921. To calculate this, you must consider that at the end of the bond's term, the investor will receive the $1,000 face value. The yield to maturity represents the total return on the bond, which includes interest payments plus capital gains. Assuming there are no coupon payments (as it is a discount bond), the formula to calculate the yield to maturity would be as follows:
- Subtract the current price of the bond ($921) from the face value ($1,000) to find the total return at maturity, which would be $79.
- Divide $79 by the current price ($921) to get the annual return.
- As the bond is held for 3 years, calculate the annual yield to maturity by taking the cube root of (1 + annual return) - 1.
Mathematically, this gives us an equation for the approximate yield to maturity (YTM):
YTM ≈ [(($1,000 / $921)^(1/3)) - 1] × 100%
Calculating this, we find that the approximate yield to maturity is 2.8% when rounded to one decimal place.