Final answer:
The duration of a zero-coupon bond matches its time to maturity, so it's 10 years, 11 years, and 12 years for the respective maturities given. When interest rates rise, the value of the bond decreases; hence, you would pay less than $10,000 for a bond one year away from its maturity when interest rates have increased to 9%.
Step-by-step explanation:
The duration of a zero-coupon bond is equal to its time to maturity. Therefore, a) for a bond with 10 years to maturity, the duration is 10 years. b) If the maturity increases to 11 years, the duration also increases to 11 years. c) Similarly, for a bond with a maturity of 12 years, the duration will be 12 years.
Regarding the scenario involving the local water company's bond, a) since interest rates have increased from 6% to 9%, you would expect to pay less than $10,000 for the bond. b) The present value of the bond can be calculated using the formula for present value of a zero-coupon bond, which is PV = F / (1 + r)^n, where PV is the present value, F is the face value, r is the interest rate, and n is the number of years until maturity. For a $10,000 bond with one year to maturity and a 9% interest rate, the bond would be worth PV = $10,000 / (1 + 0.09)^1 = $9,174.31 (rounded to two decimal places).
The duration of a zero-coupon bond is the weighted average of the time until each payment is received, weighted by the present value of each payment. Since a zero-coupon bond has no periodic interest payments, the duration of the bond is equal to its time to maturity.
a. For a zero-coupon bond with ten years to maturity, the duration is 10 years.
b. If the maturity increases to 11 years, the duration would also increase to 11 years.
c. If the maturity increases to 12 years, the duration would increase to 12 years as well.