Final answer:
The bond least sensitive to interest rate changes is the 4-year; 4 percent coupon bond. If interest rates rise from the original rate, bonds previously issued will sell for less than face value. In the given scenario, you would expect to pay less than $10,000 for the bond, with the calculation showing an amount of approximately $9724.77.
Step-by-step explanation:
The value of the bond least sensitive to fluctuations in interest rates is the 4-year; 4 percent coupon bond. When comparing the sensitivity of bonds to interest rate changes, one must consider duration and coupon rate. Duration measures the length of time until the bond's cash flows, such as coupons and principal repayment, are returned to the investor. The longer the duration, the more sensitive the bond is to interest rate changes. Furthermore, bonds with lower coupon rates tend to have higher durations, making them more sensitive to interest rates. Both factors considered, the 4-year bond with a lower coupon rate of 4 percent is less sensitive compared to higher duration or higher coupon bonds in the given choices.
To address the second part of the question, when interest rates rise from the bond's original rate, existing bonds issued at lower rates become less valuable, thus they sell for less than face value. As interest rates have risen to 9% from the original 6%, one would expect to pay less than the $10,000 face value for the bond. The calculation would involve finding the present value of the bond's remaining cash flows (final year's coupon plus principal repayment) discounted at the new interest rate of 9%.
Assuming the bond pays an annual coupon and the market interest rates are compounded annually, the bond has one coupon payment of $600 (6% of $10,000) and a principal repayment of $10,000 in one year. The present value of this bond at the 9% market interest rate would be:
$600 / (1 + 0.09) + $10,000 / (1 + 0.09) = $550.46 + $9174.31 = $9724.77
Thus, you would be willing to offer approximately $9724.77 for the bond now.