How does the age at which a person starts saving impact the total amount they can earn through compound interest, assuming the same interest rate and annual contributions?

• A. Compound interest only benefits those who start saving after age 40.
• B. The age at which a person starts saving has no impact on the total amount earned from compound interest.
• C. Starting to save later in life results in a higher total amount earned due to higher interest rates.
• D. Starting to save at a younger age allows more time for compound interest to accumulate, resulting in a higher total amount earned.

Answer: (D)

Verified step by step guidance

1. Understand the concept of compound interest: Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is: $A=P(1+r){\left(}^n$, where A is the future value, P is the principal amount, r is the annual interest rate, and n is the number of compounding periods.
2. Recognize the importance of time in compound interest: The longer the time period (n), the more compounding periods there are, which allows the interest to accumulate on both the principal and the previously earned interest.
3. Compare scenarios: If a person starts saving at a younger age, they have more compounding periods compared to someone who starts saving later. This results in a higher total amount earned due to the exponential growth of compound interest over time.
4. Debunk misconceptions: Starting to save later in life does not result in a higher total amount earned unless the interest rate or contributions are significantly higher, which is not stated in the problem. Similarly, compound interest benefits everyone regardless of age, as long as they save and invest.
5. Conclude the correct answer: Starting to save at a younger age allows more time for compound interest to accumulate, resulting in a higher total amount earned. This highlights the importance of early financial planning and saving.