Answer:
$893.93.
Step-by-step explanation:
To calculate the price you would receive if you sold your bond when interest rates rise to 8%, you need to use the concept of bond valuation. The value of a bond is the present value of its future cash flows, which include the interest payments and the principal repayment at maturity. The present value of these cash flows depends on the current interest rates and the time remaining until the bond matures.
To begin, we need to calculate the present value of the bond's future cash flows at the current interest rate of 5%. The bond pays 5% annual interest on a $1,000 face value, so the annual interest payment is $50. The bond matures in 20 years, so the total number of interest payments is 20. We can use the formula for present value of an annuity to calculate the present value of these cash flows:
PV = PMT x [1 - 1/(1+r)^n] / r
where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of payments.
Plugging in the values, we get:
PV = $50 x [1 - 1/(1+0.05)^20] / 0.05
PV = $50 x [1 - 0.3769] / 0.05
PV = $853.88
So the present value of the bond's future cash flows at the current interest rate of 5% is $853.88.
Now, we need to calculate the present value of the bond's future cash flows at the new interest rate of 8%. Using the same formula, we get:
PV = $50 x [1 - 1/(1+0.08)^20] / 0.08
PV = $50 x [1 - 0.1735] / 0.08
PV = $679.38
So the present value of the bond's future cash flows at the new interest rate of 8% is $679.38.
To find the price you would receive if you sold the bond, you simply need to add up the present value of the future interest payments and the present value of the principal repayment at maturity:
Price = PV of interest payments + PV of principal repayment
Price = $50 x [1 - 1/(1+0.08)^20] / 0.08 + $1,000 / (1+0.08)^20
Price = $679.38 + $214.55
Price = $893.93
Therefore, if interest rates rise to 8% and you sell your bond, you would receive a price of approximately $893.93.