Final answer:
The present value of the bond is calculated by discounting future payments back to their current worth. With an 8% discount rate, the bond value would be $3,064.81. If the discount rate rises to 11%, the new bond value decreases to $2860.35.
Step-by-step explanation:
Calculating Bond Value and the Impact of Changing Discount Rates
To calculate the present value of a bond, we examine the future payments it will make and discount them back to their current worth. For a $3,000 bond with an 8% interest rate, the bond will pay $240 in interest each year for two years, and repay the $3,000 principal at the end. Using a discount rate equal to the interest rate of 8%, the present value of the first year's interest is $240 / (1 + 0.08) = $222.22, and the present value of the second year's interest and principal is ($240 + $3,000) / (1 + 0.08)^2 = $2842.59. The bond's value would be the sum of these present values, totaling to $3,064.81. If the discount rate rises to 11%, then the present value calculations change to $240 / (1 + 0.11) = $216.22 for the first year and ($240 + $3,000) / (1 + 0.11)^2 = $2644.13 for the second year, giving a new bond value of $2860.35.
When interest rates rise, and the bond discount rate is adjusted accordingly, the bond value decreases as future payments are discounted more heavily. Conversely, if interest rates were to fall, the bond's value would increase, as future payments would be discounted less. This inversely proportional relationship between interest rates and bond value is fundamental to bond investing.