Final answer:
The value of a $10,000 bond with a 6% interest rate will decrease in a market where interest rates have risen to 8%. The bond's current value can be calculated by discounting its future cash flows by the new interest rate, resulting in a value less than the face value due to the higher available market rates.
Step-by-step explanation:
Bond Valuation in Response to Interest Rate Changes
When the general market interest rates rise, the value of existing bonds that were issued at lower interest rates typically decreases. This inverse relationship is due to investors being able to receive a higher return on new bonds, making the older, lower-interest bonds less attractive unless they can be purchased at a lower price.
Let's consider a $10,000 bond with a 6% interest rate in a market where rates have increased to 8%. To determine the value of the bond, we calculate the present value of its future cash flows (the interest payments and the principal repayment) discounted at the current market rate of 8%. Given that this scenario deals with a bond one year from maturity, the only cash flow would be the final interest payment and the repayment of the principal.
Calculating the Bond's Current Value
- The bond will pay $600 in interest (6% of $10,000) in one year.
- The principal of $10,000 will also be repaid in one year.
- The total payment in one year is $10,600.
- To find the current value, we discount this amount by the new interest rate of 8%: Present Value = $10,600 / (1 + 0.08) = $9,814.81.
Therefore, given the rise in interest rates to 8%, the bond's value would be less than the face value, specifically $9,814.81, which reflects the current market conditions.