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The relationship between future value and present value is rooted in the concept of time value of money, which recognizes that money has the potential to grow over time due to interest. The correct characterization is that future value increases as both the present value and the interest rate rise.

When you have an initial sum of money (the present value), investing it or allowing it to accrue interest means that it will increase in worth over a specific period. The greater the initial investment (present value), the higher the future amount will be once interest is applied. Additionally, as the interest rate increases, the amount of growth on that initial investment also escalates, leading to a higher future value. Thus, the interplay of present value and interest rate significantly influences the future value, making the assertion that it increases with both factors accurate.

In contrast, future value can be either equal to, greater than, or less than present value depending on the interest rate and time frame considered. Future value equaling present value is plausible only when the interest rate is zero or when considering the present value at a point in time. Therefore, simply stating that future value can never equal present value ignores these nuances.

This understanding of time-value calculations is crucial in finance and investment decisions, highlighting