Which expression represents simple interest earned on principal P at decimal annual rate r for t years?

Which expression represents simple interest earned on principal P at decimal annual rate r for t years?

• A. P*r*t
• B. P*(1+r)^t
• C. P*r*t/100
• D. P + r*t

Answer: (A)

Simple interest is earned by applying the rate to the original principal each year. If the rate r is in decimal form, the interest earned over t years is P × r × t. This direct multiplication captures how much extra money the principal generates over time. The chosen expression matches this idea exactly. The other forms describe different scenarios: compounding (P × (1 + r)^t) grows the amount in a non-linear way, using a percent-rate form would require dividing by 100 (P × r × t / 100), and adding the principal back (P + r × t) gives the total amount, not just the interest itself.

Simple interest is earned by applying the rate to the original principal each year. If the rate r is in decimal form, the interest earned over t years is P × r × t. This direct multiplication captures how much extra money the principal generates over time.

The chosen expression matches this idea exactly. The other forms describe different scenarios: compounding (P × (1 + r)^t) grows the amount in a non-linear way, using a percent-rate form would require dividing by 100 (P × r × t / 100), and adding the principal back (P + r × t) gives the total amount, not just the interest itself.