Final answer:
The current value of a two-year bond with an 8% interest rate decreases when the discount rate increases from 8% to 11% due to the lower present value of future cash flows at the higher discount rate.
Step-by-step explanation:
To calculate the current value of a two-year bond issued at $3,000 with an interest rate of 8%, we first calculate the cash flows: $240 of interest at the end of the first year and $3,240 at the end of the second year (which is the $240 interest plus the $3,000 principal). To find the present value of these cash flows at the initial 8% discount rate, we use the present value formula:
- PV = C1/(1+r)^1 + C2/(1+r)^2
- PV = $240/(1+0.08)^1 + $3,240/(1+0.08)^2
- PV = $240/1.08 + $3,240/1.08^2
- PV = $222.22 + $2,777.78
- PV = $3,000
If the discount rate rises to 11%, the new present values are:
- PV = $240/(1+0.11)^1 + $3,240/(1+0.11)^2
- PV = $240/1.11 + $3,240/1.11^2
- PV = $216.22 + $2,630.63
- PV = $2,846.85
Therefore, the bond's worth decreases if the discount rate increases from 8% to 11% because the present value of future cash flows decreases when discounted at a higher rate.