Final answer:
The present value of a two-year bond with a payment of $240 in both years and a $3,000 principal in the second year using an 8% discount rate is calculated by discounting each payment to today's dollars, yielding a present value of $3,000. If the discount rate increases to 11%, the present value must be recalculated using this new rate.
Step-by-step explanation:
To calculate the present value (PV) of a bond or an annuity, we need to discount the future payments to their equivalent value in today's dollars. The discount rate is the rate of interest that would be earned on an investment over a specified period. For a simple two-year bond with an annual interest rate of 8% and payments of $240 in the first year and $240 plus the $3,000 principal in the second year, the present value can be caluclated as:
- First Year's Payment PV: $240 / (1 + 0.08)¹ = $222.20
- Second Year's Payment PV: $3,240 / (1 + 0.08)² = $2,777.80
- Total PV = First Year's PV + Second Year's PV = $222.20 + $2,777.80 = $3,000
If the discount rate changes to 11%, the new present value would need to be calculated using this higher rate to reflect the increased opportunity cost due to the rise in interest rates.