Simple Interest & Compound Interest
Interest is the cost of borrowing money — or the reward for saving it. On the SAT, you'll encounter problems involving both simple interest and compound interest. Understanding the difference between these two models is essential for scoring well on the test.
📐 Simple Interest
Simple interest is calculated only on the original principal (the initial amount). The interest earned each period is always the same.
Formula
A = P(1 + rt)
- A = Final amount (principal + interest)
- P = Principal (initial investment/loan)
- r = Annual interest rate (as a decimal)
- t = Time (in years)
Interest only:
I = Prt
Growth is linear — the graph is a straight line.
📈 Compound Interest
Compound interest is calculated on the principal PLUS all previously accumulated interest. Your money earns "interest on interest."
Formula
A = P(1 + r/n)nt
- A = Final amount
- P = Principal (initial amount)
- r = Annual interest rate (as a decimal)
- n = Number of times compounded per year
- t = Time (in years)
Common compounding frequencies:
Annually: n=1 | Semi-annually: n=2 | Quarterly: n=4 | Monthly: n=12 | Daily: n=365
Growth is exponential — the graph curves upward.
📊 Visual Comparison: Simple vs. Compound Interest
The chart below shows how $1,000 grows over 20 years at 8% interest — one with simple interest (linear) and one with compound interest (exponential). Notice how the gap widens dramatically over time.