Final answer:
The present value calculated using the nominal interest rate is lower when the interest rate is higher. An increase in interest rates leads to a decrease in the present value of future cash flows. This is due to the time value of money, as investors could get higher returns from new bonds issued at the current higher rates.
Step-by-step explanation:
The correct answer to the question which is higher, the present value calculated using the nominal interest rate or the discount rate, for a given annual effective discount rate, is option a. The present value calculated using the nominal interest rate is lower because the interest rate is higher than the nominal discount rate for the given annual effective discount rate.
When the interest rate increases, as per the given scenario from 8% to 11%, the present value of future cash flows (like bond payments) decreases. This is because the present value is the current worth of future cash payments discounted at the current interest rate.
If the current interest rate is higher, it takes less present dollars to equate to the same future dollars due to the time value of money principle.
When you have a bond, and interest rates rise after its issuance, the bond will sell for less than its face value because the interest rate associated with it is lower than the current prevailing rates. This means that the bond is less valuable to an investor since they could receive higher interest payments from newly issued bonds.
The present value calculations reflect these differences in interest rates and demonstrate why the value of the bond decreases when interest rates rise.