Final answer:
To compute the present value of a simple two-year bond with a face value of $3,000 and an 8% interest rate, present value calculations are performed for each payment. The calculations are first done using an 8% discount rate and then readjusted for a new 11% rate. The sum of the present values of the payments gives us the total current worth of the bond at each respective discount rate.
Step-by-step explanation:
When analyzing a simple two-year bond issued for $3,000 with an 8% interest rate, the yearly interest would be $240. This results in a payment of $240 after the first year and a combined payment of principal plus interest totaling $3,240 at the end of the second year. To determine the present value of this bond with a discount rate of 8%, we use the present value formula for each payment:
First Year Interest: $240 / (1 + 0.08)1 = $222.20
Second Year Total (Interest + Principal): $3,240 / (1 + 0.08)² = $2,777.80
Adding both present values together yields the total present value of the bond when the discount rate is 8%.
If the discount rate increases to 11%, the calculations are adjusted with the new rate:
First Year Interest: $240 / (1 + 0.11)1 = $216.22
Second Year Total (Interest + Principal): $3,240 / (1 + 0.11)² = $2,620.77
The new total present value is the sum of these two new present values when the discount rate is 11%.