How does an increase in the interest rate affect the amount of money earned on a savings account over time, assuming all other factors remain constant?

• A. It decreases the amount of money earned because less interest is paid.
• B. It causes the money earned to fluctuate unpredictably.
• C. It has no effect on the money earned; only the initial deposit matters.
• D. It increases the amount of money earned due to higher interest accumulation.

Answer: (D)

Verified step by step guidance

1. Understand the concept of interest rate: The interest rate is the percentage at which money in a savings account grows over time. Higher interest rates mean that the principal amount earns more interest, leading to greater accumulation of money.
2. Identify the type of interest: Determine whether the savings account uses simple interest or compound interest. Compound interest typically results in faster growth because interest is earned on both the principal and previously accumulated interest.
3. Analyze the relationship between interest rate and earnings: As the interest rate increases, the amount of interest earned on the principal also increases, assuming all other factors remain constant.
4. Consider the formula for interest calculation: For simple interest, the formula is \( I = P \times r \times t \), where \( I \) is the interest earned, \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time period. For compound interest, the formula is \( A = P \times (1 + r)^t \), where \( A \) is the total amount after interest, \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time period.
5. Conclude the effect of an increased interest rate: Higher interest rates lead to greater interest accumulation over time, increasing the total amount of money earned in the savings account.