How to Calculate Compound Interest — Formula & Examples
Compound interest is often called the eighth wonder of the world — earning interest on your interest creates exponential growth over time. Understanding how it works is fundamental to making smart decisions about savings, investments, and debt. The same force that grows your savings account also works against you on a credit card balance.
Simple Interest vs Compound Interest
Simple interest is calculated only on the original principal. If you invest $1,000 at 5% simple interest for 10 years, you earn $50 per year = $500 total, ending with $1,500.
Compound interest is calculated on the principal plus all previously earned interest. The same $1,000 at 5% compound interest for 10 years grows to $1,628.89 — an extra $128.89 just from compounding.
The Compound Interest Formula
A = P(1 + r/n)^(nt)
A = Final amount · P = Principal · r = Annual rate (decimal) · n = Compounds per year · t = Time in years
Example: $5,000 at 6% compounded monthly for 10 years:
A = 5000(1 + 0.06/12)^(12×10) = 5000(1.005)^120 = 5000 × 1.8194 = $9,096.98
Compounding Frequency Matters
| Frequency | n value | $10,000 at 5% for 10 years |
|---|---|---|
| Annually | 1 | $16,288.95 |
| Semi-annually | 2 | $16,436.19 |
| Quarterly | 4 | $16,436.19 |
| Monthly | 12 | $16,470.09 |
| Daily | 365 | $16,486.65 |
More frequent compounding produces slightly better results, but the differences are smaller than many people expect. Going from annual to daily compounding adds about $200 over 10 years on $10,000 at 5%.
The Rule of 72
The Rule of 72 is a simple mental math trick to estimate how long it takes for an investment to double: divide 72 by the annual interest rate. At 6% interest, money doubles in approximately 72 ÷ 6 = 12 years. At 9%, it doubles in about 8 years. At 3%, it doubles in about 24 years.
Rule of 72: Years to double = 72 ÷ Annual Interest Rate (%)
Compound Interest Working Against You
Credit cards typically charge 18-29% APR, compounded daily. On a $3,000 balance at 24% APR with no payments, after one year you'd owe $3,726 — nearly $726 in interest. After five years with minimum payments only, you could end up paying thousands more than the original balance. The math of compound interest is identical whether it's working for you (savings) or against you (debt).
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