Final answer:
To find the present value of a New York state bond with a $1,000 payoff in ten years at a 5% interest rate, the formula for present value yields $613.91, making it worth less than its face value today. When market interest rates rise, the value of existing bonds with lower rates decreases, so one would pay less than the face value for a bond in such a scenario. Therefore correct option is A
Step-by-step explanation:
The value of a bond can be calculated using the present value of its future cash flows, which are discounted at the current market interest rate. To determine the value of a New York state bond that will pay $1,000 ten years from now at a market interest rate of 5.0%, we use the formula for the present value of a single future cash flow:
PV = FV / (1 + r)^n
Where:
- PV is the present value of the bond.
- FV is the future value of the bond, which in this case is $1,000.
- r is the interest rate (5.0% or 0.05).
- n is the number of years until the bond matures, which is 10.
Substituting these values into the formula gives:
PV = $1,000 / (1 + 0.05)^10
= $1,000 / 1.62889
= $613.91
Therefore, the present value of the bond today is $613.91.
In the scenario where the interest rates increased from 6% to 9% for a local water company's ten-year bond, you would expect to pay less than the face value of $10,000 for the bond due to the inverse relationship between bond prices and interest rates. Since the bond's fixed interest payments are now lower compared to the new interest rate, the price of the bond must decrease to make it attractive to new investors.
Calculating the exact price requires discounting the final year's cash flows at the new market interest rate of 9%.