Final answer:
To determine the amount of systematic annuitization, the Assumed Interest Rate (AIR) is typically used. For bonds, the price varies inversely with market interest rates, so an increase in rates often leads to paying less than the face value of the bond, while a decrease in rates could mean paying more.
Step-by-step explanation:
The determined amount of systematic annuitization is often calculated using the Assumed Interest Rate (AIR). When it comes to annuities, the AIR is used to determine the future payments that the annuity will provide, based on the amount of principal invested and the duration of the annuity. However, real-world calculations for determining the present value of future payments, such as bonds, can be more complex as they involve considering the market interest rate and the issuer's creditworthiness. If the market interest rates increase, the price of existing bonds typically decreases, and vice versa.
Therefore, if interest rates have risen since a bond was issued, one would generally expect to pay less than the bond's face value of $10,000, as investors would need a higher yield to match current market rates. Conversely, if interest rates have fallen, the bond could be worth more than $10,000, because its fixed interest payments are more attractive compared to the new lower rates available in the market.