Final answer:
The statement is true; the future value of money grows over time at a given positive interest rate due to compound interest.
Step-by-step explanation:
The statement that for a given positive interest rate, the future value of $100 increases with the passage of time is true. This is because the concept of compound interest means that interest is earned on both the initial principal and the interest that has been added to that principal over time. However, changes in interest rates can affect the present and future value differently.
For example, if you own a bond that pays 8% interest, but new bonds are issued at a higher rate of 12%, the present value of your bond's future payments discounted at the new higher rate will be lower. Despite the actual future payments not changing, the rising interest rates mean that your bond's market value falls because new investors can get a better rate elsewhere.
If we discuss present discounted value, we must understand that it represents how much a future amount is worth today given a specific interest rate. For instance, if the interest rate is 25%, then a future payment of $125 in one year is equivalent to $100 today, because $100 invested at that rate would grow to $125 over that year.