Final answer:
The investor's annualized return for a 5-year zero coupon bond purchased at $2,000 with a face value of $2,500 is approximately 4.5% when using a simple interest model.
Step-by-step explanation:
The return provided to the investor for a 5-year zero coupon bond with a face value of $2,500 that sells for $2,000 can be calculated using the formula for the annualized return on investment (ROI). This bond, which is a type of pure discount bond, does not pay periodic interest payments but is sold at a discount, with the face value being received at maturity. To calculate the investor's return, we use the formula:
ROI = (Face Value - Purchase Price) / Purchase Price
And then annualize it over the period of the bond, which is 5 years in this case. So:
ROI = ($2,500 - $2,000) / $2,000 = $500 / $2,000 = 0.25 or 25%
To annualize the ROI, we consider the 5-year term and use the formula for the annualized return:
Annualized Return = (1 + ROI)^(1/n) - 1
Where n is the number of years. Plugging our values in:
Annualized Return = (1 + 0.25)^(1/5) - 1 ≈ 0.045 or 4.5%
Therefore, the annualized return on this zero coupon bond is approximately 4.5%. We assume here a simple interest model and do not take compounding into account. This means the investor earns a return of about 4.5% per year.