Final answer:
The present value of a simple two-year bond with an 8% interest rate and a $3,000 face value is calculated using the present value formula. It equals approximately $3,000 when the discount rate is also 8%. If the discount rate rises to 11%, the present value decreases to approximately $2,850.59.
Step-by-step explanation:
The question appears to involve calculating the present value of a bond that pays interest and returns the principal at the end. Specifically, we are dealing with a simple two-year bond that pays 8% interest per year and has a face value of $3,000.
To calculate the present value, we apply the present value formula for each cash flow and sum these amounts. For the first year interest payment of $240, the present value is calculated by discounting this amount by the 8% interest rate, which yields:
$240 / (1 + 0.08)¹ = $222.22
For the second year, we not only have the $240 interest payment, but also the return of the $3,000 principal. These are both discounted back to present value:
$240 / (1 + 0.08)² = $204.62 (rounded)
$3,000 / (1 + 0.08)² = $2,573.19 (rounded)
The total present value is thus the sum of these individual present values, which gives us:
$222.22 + $204.62 + $2,573.19 = $3,000.03 (rounded)
In case of the interest rates rising to 11%, the calculation will be similar, but using 11% as the discount rate:
$240 / (1 + 0.11)¹ = $216.22 (rounded)
$240 / (1 + 0.11)² = $194.81 (rounded)
$3,000 / (1 + 0.11)² = $2,439.56 (rounded)
The total present value in this scenario would be:
$216.22 + $194.81 + $2,439.56 = $2,850.59 (rounded)