Final answer:
The present value of a two-year bond with a $3,000 principal at an 8% interest rate is $3,000 when discounted at 8%, and if interest rates rise causing the discount rate to increase to 11%, the present value is $2,847.
Step-by-step explanation:
The question involves calculating the present value of a simple two-year bond with a principal amount of $3,000 and an annual interest rate of 8%. To find the present value, we use the formula: PV = P / (1 + r)^n, where PV is the present value, P is the future payment, r is the discount rate, and n is the number of periods.
First, calculate the present value with an 8% discount rate:
- Year 1 interest payment: PV = $240 / (1 + 0.08)^1 = $240 / 1.08 = $222.22
- Year 2 interest + principal: PV = ($240 + $3,000) / (1 + 0.08)^2 = $3,240 / 1.1664 = $2,777.78
Next, sum up the present values for both years to get the total present value at 8% discount rate: $222.22 + $2,777.78 = $3,000.
If the discount rate increases to 11%, recalculate as follows:
- Year 1 interest payment: PV = $240 / (1 + 0.11)^1 = $240 / 1.11 = $216.22
- Year 2 interest + principal: PV = ($240 + $3,000) / (1 + 0.11)^2 = $3,240 / 1.2321 = $2,630.64
The total present value at 11% discount rate is: $216.22 + $2,630.64 = $2,846.86. Rounded to the nearest whole dollar, it is $2,847. The present value is the value of future cash flows discounted back to their value today, considering the discount rate.