Financial Planning5 min read•Updated 2026-09-04
Compound Interest Formula & Wealth Growth: How Compounding Works
Understand the math behind compound interest, calculate future investment values, and compare compounding frequencies.
MX
MultiToolX Technical Team
Financial Engineering
Key Takeaways
- The compound interest formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is principal, r is rate, n is compounding frequency, and t is time in years.
- More frequent compounding (daily or monthly vs annually) yields a higher effective annual rate (EAR).
- The Rule of 72 provides a quick mental calculation: divide 72 by your annual interest rate to find how many years it takes to double your money.
1. Compound Interest vs Simple Interest
Simple interest earns returns strictly on the initial principal. Compound interest earns returns on the initial principal plus all previously accumulated interest. Over long periods (10-30 years), compounding creates exponential wealth growth.
2. The Compound Interest Formula
The mathematical formula is:
A = P * (1 + r/n)^(n*t)
Where:
- A = Final total balance
- P = Initial deposit or principal
- r = Annual nominal interest rate (in decimal format, e.g. 7% = 0.07)
- n = Number of times interest compounds per year (Monthly: 12, Quarterly: 4, Annually: 1)
- t = Number of years invested
Frequently Asked Questions
What is the Rule of 72?
Divide 72 by the annual return rate. At 8% annual return, your money doubles in approximately 9 years (72 / 8 = 9).
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