Final answer:
Assuming a positive interest rate, the present value of future payments is less than their future dollar amount because present value calculations discount future payments by the interest rate. Rising interest rates lead to lower present values for those future payments and reduce the market value of investments like bonds.
Step-by-step explanation:
Assuming a positive interest rate, the present value of a future payment is less than its future dollar amount. This is because the present value is calculated by discounting future payments back to their value today, using the prevailing interest rate as the discount rate. If interest rates increase, as in the example where they go from 8% to 11%, the present value of the same future payments decreases, highlighting the impact of interest rate risk. For instance, a future payment of $125 discounted at an interest rate of 25% has a present value of only $100 today because you could invest $100 at the 25% interest rate to obtain $125 in the future.
Additionally, when the market interest rate rises, bonds paying lower rates, like our example with an 8% rate, become less attractive compared to new bonds paying higher rates. Consequently, the selling price (or market value) of the older bonds falls, resulting in a loss for those who attempt to sell before maturity.