How do compound interest and simple interest differ?

How do compound interest and simple interest differ?

• A. Compound interest accrues on initial principal plus accumulated interest; simple interest accrues only on the principal.
• B. Compound interest accrues only on principal; simple accrues on accumulated interest.
• C. Both accrue on all assets equally.
• D. Simple interest compounds more quickly.

Answer: (A)

The idea being tested is how interest is calculated over time. Simple interest uses only the original amount invested (the principal) to compute each period’s earning, while compound interest uses the growing balance, so interest earns interest itself. In simple interest, each period adds the same amount: interest = principal × rate × time. So the total grows linearly with time. In compound interest, interest is added to the balance, and next period’s interest is calculated on that larger amount. This makes the balance grow exponentially over time: A = principal × (1 + rate)^(time) (for annual compounding, with adjustments for other frequencies). For example, on $1,000 at 5% for 3 years: - Simple interest: $1,000 × 0.05 × 3 = $150 in interest; total $1,150. - Compound interest (annually): $1,000 × (1.05)^3 ≈ $1,157.63; interest ≈ $157.63. That’s why the statement that compound interest accrues on the initial principal plus accumulated interest is correct, while simple interest accrues only on the principal. The other choices don’t fit: compound interest does not accrue only on principal, both do not accrue equally on all assets, and simple interest does not compound—its growth is slower.

The idea being tested is how interest is calculated over time. Simple interest uses only the original amount invested (the principal) to compute each period’s earning, while compound interest uses the growing balance, so interest earns interest itself.

In simple interest, each period adds the same amount: interest = principal × rate × time. So the total grows linearly with time.

In compound interest, interest is added to the balance, and next period’s interest is calculated on that larger amount. This makes the balance grow exponentially over time: A = principal × (1 + rate)^(time) (for annual compounding, with adjustments for other frequencies).

For example, on $1,000 at 5% for 3 years:

• Simple interest: $1,000 × 0.05 × 3 = $150 in interest; total $1,150.

• Compound interest (annually): $1,000 × (1.05)^3 ≈ $1,157.63; interest ≈ $157.63.

That’s why the statement that compound interest accrues on the initial principal plus accumulated interest is correct, while simple interest accrues only on the principal. The other choices don’t fit: compound interest does not accrue only on principal, both do not accrue equally on all assets, and simple interest does not compound—its growth is slower.