Final answer:
The statement is false. More frequent compounding of interest leads to a lesser amount needing to be invested today to reach a certain future value, as compound interest grows on both the initial principal and accumulated interest over time.
Step-by-step explanation:
The statement that 'the more frequently interest is compounded, the greater the amount of money that has to be invested today in order to accumulate a given future amount' is actually false. In fact, the opposite is true.
The more frequently interest is compounded, the less money you have to invest today to accumulate a certain amount in the future. This is because compound interest earns interest not only on the initial principal but also on the interest that has been added to that principal. Therefore, frequent compounding (such as daily or monthly) results in interest being calculated on a constantly growing base, which amplifies the effect of compound interest over time.
For example, if you want to reach a future savings goal, and interest is compounded more often, each compounding period adds more interest to your savings, which then earns interest in the next period.
This accelerated growth means you can start with a smaller initial investment to reach the same future value. Hence, the benefit of compound interest can be maximized by starting to save early and allowing the principle to grow over a longer period, thereby taking full advantage of the effect of compounding over time.