Final answer:
The smallest value less than 25% among the provided options is C) 0.0211. Understanding the relationship between percentages and decimals is crucial in financial mathematics, as evidenced by the power of compound interest over time.
Step-by-step explanation:
The question asks which value is less than 25%, with the options being A) 0.0215 B) 0.022 C) 0.0211 D) 0.0225. To understand this, recall that 25% as a decimal is 0.25, so any value less than that is less than 25%. By comparing the given numbers we can see that:
- 0.0215 is less than 0.25,
- 0.022 is less than 0.25,
- 0.0211 is less than 0.25,
- 0.0225 is less than 0.25 but is the closest to 0.25.
Therefore, all options except D are less than 0.25. However, the smallest value is 0.0211, which corresponds to option C.
Understanding how percentages and decimals relate is essential in mathematics, and particularly in financial contexts such as compound interest, savings growth, and investment returns. By starting to save money early and taking advantage of compound interest, you give your savings more potential for growth. This concept is demonstrated by the formula for compound interest, which shows how an initial sum can grow over time, such as a $3,000 investment growing to $44,923 over 40 years at a 7% annual rate.