Final answer:
The statement is true; the future value of an investment increases with higher interest rates or longer investment periods due to the effects of compounding. Increased time or rates amplify the growth, depicted in the formula for computing future value.
Step-by-step explanation:
The statement that the future value increases with increases in the interest rate or the period of time funds are left on deposit is true. This is because future value is calculated by multiplying the present value by one plus the interest rate, raised to the power of the number of years.
For example, let's consider a scenario where a payment of $15 million is made now, $20 million in one year, and $25 million in two years. If the interest rate is increased from 8% to 11%, the present value of these future payments will indeed decrease since the discount rate has increased. On the other hand, if you are looking at the future value, an increase in either the interest rate or the investment period will result in a larger future value.
To clarify, future value represents how much a sum of money today will grow over a given period of time when invested at a specific interest rate. Increased time or higher interest rates compound the growth of the investment, leading to higher future values when these variables rise. Thus, while the present value of future payments decreases when the interest rate increases, the future value of an investment made today will increase with a higher interest rate or a longer investment period.