Final answer:
The present value of a two-year bond with an 8% interest rate is calculated using a discount rate to determine the current worth of future payments. At an 8% discount rate, the bond's present value equals the initial $3,000. If the discount rate increases to 11%, the present value drops to $2,842.80.
Step-by-step explanation:
Present Value of a Two-Year Bond
To calculate the present value of a simple two-year bond issued for $3,000 with an annual interest rate of 8%, we must discount the future cash flows at the current discount rate. At an 8% interest rate, the bond pays $240 at the end of the first year and $3,240 ($3,000 principal + $240 interest) at the end of the second year. The formula for the present value is PV = C / (1+r)^n, where C is the cash flow, r is the discount rate, and n is the number of periods.
Present Value at 8% discount rate:
Year 1: PV = $240 / (1 + 0.08) = $222.22
Year 2: PV = $3,240 / (1 + 0.08)^2 = $2777.78
Combined Present Value = $222.22 + $2777.78 = $3,000
If the discount rate rises to 11%, new calculations are:
Year 1: PV = $240 / (1 + 0.11) = $216.22
Year 2: PV = $3,240 / (1 + 0.11)^2 = $2626.58
Combined Present Value = $216.22 + $2626.58 = $2,842.80