Question

1. one account pays 3.3% simple interest annually. the other pays 2.6% compound interest annually. which statement is true? a. simple interest grows faster b. compound interest grows faster over time c. both accounts earn the same d. neither account earns interest

Explanation:

Step1: Recall Interest Formulas

Simple Interest: $I = P \times r \times t$, where $P$ is principal, $r$ is rate, $t$ is time.
Compound Interest: $A = P(1 + r)^t$, interest is $A - P$.

Step2: Analyze Growth Rates

• Simple interest grows linearly (constant rate on principal).
• Compound interest grows exponentially (interest earns interest, so rate applies to principal + accumulated interest). Over time, exponential growth (compound) outpaces linear (simple), even if initial simple rate is higher (3.3% vs 2.6% here).

Step3: Evaluate Options

• A: False (compound grows faster over time).
• B: True (compound’s exponential growth surpasses simple’s linear growth as $t$ increases).
• C: False (different growth patterns, earnings differ).
• D: False (both earn interest by definition).

Answer:

B. Compound interest grows faster over time