Explain the relationship between interest rates and present value.

The relationship between interest rates and present value is inverse. In other words, as interest rates increase, the present value of future cash flows decreases, and vice versa.

Present value is a financial concept that calculates the current worth of future cash flows by discounting them back to the present using an appropriate interest rate. The rationale behind this concept is that money received in the future is worth less than the same amount of money received today due to the opportunity cost of not having that money available for investment or consumption immediately.

When interest rates are higher, the opportunity cost of not having the money today is greater. Therefore, the present value of future cash flows decreases because the discounting factor applied to those cash flows is larger. This means that the future cash flows are worth less in today's terms.

Conversely, when interest rates are lower, the opportunity cost of not having the money today is lower. As a result, the present value of future cash flows increases because the discounting factor applied to those cash flows is smaller. This means that the future cash flows are worth more in today's terms.

To illustrate this relationship, consider a simple example. Let's say you have the option to receive $1,000 one year from now. If the interest rate is 5%, the present value of this future cash flow would be calculated as follows:

Present Value = Future Value / (1 + Interest Rate)
Present Value = $1,000 / (1 + 0.05)
Present Value = $952.38

Now, if the interest rate increases to 10%, the present value of the same future cash flow would be calculated as follows:

Present Value = $1,000 / (1 + 0.10)
Present Value = $909.09

As you can see, the higher interest rate reduces the present value of the future cash flow. This relationship holds true for any future cash flows, whether they are single payments or a series of cash flows over time.

In summary, the relationship between interest rates and present value is inverse. Higher interest rates result in lower present values, while lower interest rates result in higher present values. This relationship is fundamental to understanding the time value of money and is widely used in various financial calculations and decision-making processes.