Final answer:
Given a future value, a lower interest rate leads to a higher present value as the future cash flows are discounted less. The higher the interest rate, the lower the present value will be, due to the principles of time value of money. An investor's choice of interest rate reflects opportunity cost, return expectations, and risk premiums.
Step-by-step explanation:
Given a future value, a lower interest rate would result in the highest present value. When calculating present value, future cash flows are discounted by an interest rate; this means that the higher the interest rate, the lower the present value, as the future cash flows are considered to be worth less today. This relationship is a fundamental principle of time value of money, which reflects the idea that money available in the present is worth more than the same amount in the future due to its potential earning capacity.
It's important to recognize that the actual dollar payments do not change with the interest rate; they are set by the terms of the financial instrument, such as a bond. However, the present value of these payments, when calculated using a higher interest rate, will indeed be lower. Conversely, a lower discount rate will make the same future payments more valuable in today's terms, resulting in a higher present value for those future cash flows.
An investor or financial analyst looking to determine the present value of an investment must consider the rate of return on other available financial opportunities, the opportunity cost of investing the capital, and as well as any risk premiums associated with the investment.