ACT Math Simple and Compound Interest: Calculate Growth Using Two Formulas

Simple interest: Interest=Principal×Rate×Time (I=PRT). The interest earned is calculated on the principal only, not accumulated interest. Example: $1000 at 5% for 2 years earns I=1000×0.05×2=$100. Total amount: $1100. Compound interest: Amount=Principal×(1+Rate)^Time (A=P(1+r)^t). Interest is calculated on the principal and accumulated interest. Example: $1000 at 5% for 2 years: A=1000×(1.05)^2=1000×1.1025=$1102.50. Recognize which type the problem describes, apply the appropriate formula, and calculate.

Key distinction: Simple interest grows linearly (constant added each period). Compound interest grows exponentially (accelerating growth). Problems usually specify "simple" or "compound," but if not, assume compound.

Mistake 1: Using simple interest when compound is intended (or vice versa). Read the problem carefully. "Interest is compounded annually" signals compound interest. Mistake 2: Converting percentage to decimal incorrectly. 5% is 0.05, not 5. This reversal causes huge errors. Mistake 3: Forgetting that Amount=Principal+Interest for simple interest. The formula I=PRT gives only interest earned, not total. Always verify whether the problem asks for interest earned (I) or total amount (P+I or A).

Create a reference card showing both formulas and one worked example of each. Reference it daily until both become automatic.

Problem 1: $2000 at 4% simple interest for 3 years. Interest=2000×0.04×3=$240. Total amount=$2240. Problem 2: $2000 at 4% compound interest for 3 years. Amount=2000×(1.04)^3=2000×1.125=$2250. Problem 3: $500 at 6% simple interest for 5 years. Interest=500×0.06×5=$150. Problem 4: $500 at 6% compound interest for 2 years. Amount=500×(1.06)^2=500×1.1236=$561.80. Problem 5: $1000 at 3% compound interest for 4 years. Amount=1000×(1.03)^4=1000×1.126=$1126. Solve all five, clearly identifying which formula applies and whether the answer is interest or total amount.

Find five interest problems from a practice test. For each, identify the type (simple or compound), apply the formula, and answer the specific question (interest earned or total amount). By the fifth problem, interest calculations will feel automatic.

Interest questions appear on some ACT Math tests, usually in questions 40-55. They test formula knowledge and calculation accuracy. Students who master both interest formulas pick up 1 point on the math section because the formulas are mechanical and application is reliable.

Drill both interest formulas daily this week. Each day, solve five problems using simple and compound interest. By test day, you should apply either formula and calculate interest or total amount within 60 seconds.