Simple & Compound Interest
Calculate simple or compound interest on savings or loans.
Formula
Simple Interest: I = P × r × t Compound Interest: A = P × (1 + r/n)^(n×t) where P = principal, r = annual rate, t = years, n = compounding periods per year
How to Calculate
Simple interest is calculated as principal multiplied by the annual rate multiplied by the time in years. It only applies to the original principal—there is no interest-on-interest effect. Simple interest is used for some short-term loans and promissory notes.
Compound interest applies interest to both the original principal and previously accumulated interest. The formula accounts for how frequently interest compounds—annually, semi-annually, quarterly, monthly, or daily. More frequent compounding results in more total interest because each calculation period adds interest to a slightly larger balance.
The difference between simple and compound interest grows dramatically over time. On a $10,000 investment at 8% over 30 years, simple interest yields $24,000 in interest ($34,000 total), while compound interest yields approximately $90,627 in interest ($100,627 total). This compounding effect is why Einstein reportedly called compound interest the "eighth wonder of the world."
Worked Example
Compare simple vs. compound interest on $25,000 at 6% for 10 years:
Simple Interest: I = $25,000 × 0.06 × 10 = $15,000 Total: $25,000 + $15,000 = $40,000
Compound Interest (monthly compounding): A = $25,000 × (1 + 0.06/12)^(12×10) A = $25,000 × (1.005)^120 A = $25,000 × 1.8194 A = $45,485 Interest earned: $45,485 − $25,000 = $20,485
Compound interest earned $5,485 more (36.6% more interest) over the same period.
Why It Matters
Understanding interest is fundamental to every financial decision—from choosing savings accounts and investments to evaluating loan offers and credit card debt. Compound interest works powerfully in your favor when saving (your money grows faster over time) but against you when borrowing (debt snowballs). Knowing the math helps you make optimal decisions on both sides.
Practical Tips
- ✓Start saving early—compound interest rewards time. A 25-year-old investing $5,000/year at 8% has $1.4 million by 65; starting at 35 yields only $611,000.
- ✓When borrowing, the compounding frequency matters—daily compounding costs more than monthly.
- ✓Use the Rule of 72 to estimate doubling time: 72 / interest rate = years to double (e.g., 72/8 = 9 years).
- ✓Compare APY (Annual Percentage Yield) rather than nominal rates for savings—APY reflects compounding.
Frequently Asked Questions
What is the Rule of 72?
What is the difference between APR and APY?
How does compounding frequency affect returns?
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