Final answer:
The statement is false because a smaller future value, given a constant present value and number of periods, generally indicates a lower interest rate was applied, not a higher rate.
Step-by-step explanation:
The statement is false. When computing an interest or growth rate, the rate will not inherently increase due to a smaller future value if the present value and the number of periods are held constant. The interest rate is a factor that determines how a present value grows over time to reach a future value. If the future value is smaller and the present value and time period remain unchanged, it would typically suggest that the interest rate applied was lower, not higher.
For example, with compound interest, the future value is calculated using the formula FV = PV(1 + r/n)^(nt), where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Therefore, if the present value (PV) and time (t) are constant and the future value (FV) decreases, it signifies that the rate (r) or the compounding frequency (n) must have decreased. This is because the formula suggests a direct relationship between the future value and the rate when the other factors are constant.