Final answer:
When interest rates increase, the price of existing bonds typically decreases to align the bond's yield with the new market rates. In the context provided, one would pay less than $10,000 for an 8% bond if market rates rise to 12%. This price adjustment reflects the present value of expected payments and compensates for the bond's lower coupon rate relative to the current market rate.
Step-by-step explanation:
The duration of a bond is a financial term that measures the sensitivity of a bond's price to changes in interest rates, by taking into account the present values of all the bond's cash flows, which include coupon payments and the repayment of the nominal value at maturity. In the given scenario, if we consider a rise in the interest rates to 12%, one would expect the price of an 8% bond to decrease below its face value to compensate for its lower yield relative to new bonds with higher interest rates. Therefore, if the bond was initially priced at $10,000, you would expect to pay less than $10,000 for the bond after the rise in interest rates, because the bond's seller must lower its price to make it an attractive investment compared to newer bonds offering 12% yield. The price adjustment ensures that the investor achieves a comparable yield to current market rates despite the bond having a lower coupon rate.
Considering the risk of the bond and assuming it carries no risk, it would typically sell at its face value. However, real-world situations are complex, and bond prices are influenced not only by the risk-free rate but also by the credit risk associated with the issuer. The described 8% bond, which is less appealing due to market rates rising to 12%, will have to be priced at a discount to compete with other investment opportunities.
When assessing investments, it's important to recognize that the price of a bond is the present value of a stream of future expected payments, adjusted for current market interest rates and the riskiness of the investment. Bond valuation is thus deeply rooted in the principles of time value of money and risk management.