Compound Interest Calculator
Compound Interest Calculator
Calculate investment growth with compound interest (A = P(1 + r/n)nt).
Report Bug Simple interest is linear; it moves like a staircase. Compound Interest is exponential; it moves like a rocket. It is the principle where the interest you earn starts earning interest itself. The Compound Interest Calculator allows you to model real-world scenarios—from High-Yield Savings Accounts (HYSA) that compound daily to Stock Market investments that compound annually.
In the US market, understanding the difference between the advertised rate (APR) and the effective rate you actually earn (APY) can mean a difference of thousands of dollars over a decade.
📈 The Wealth Formula
The calculation accounts for how many times per year the interest is added to the principal. The standard formula used by US banks is:
Variables Defined:
- P (Principal): The starting amount.
- r (Annual Rate): The interest rate as a decimal (e.g., 0.05).
- n (Frequency): Times compounded per year (12 = Monthly, 365 = Daily).
- t (Time): Duration in years.
🏦 Scenario: The Power of Frequency
Let's invest $10,000 at a 5% Interest Rate for 10 Years. Does it matter if the bank compounds the interest Once a Year vs. Every Day?
Investment Strategy: When saving (HYSA, CDs), look for Daily Compounding to maximize growth. When borrowing (Mortgages), look for Monthly or Annual compounding to minimize cost.
US Banking Standards: APR vs. APY
- APR (Annual Percentage Rate): This is the "Simple" rate. It does not account for compounding. Lenders often advertise this because it looks lower on debt.
- APY (Annual Percentage Yield): This is the "Real" rate you earn or pay after compounding. Banks advertise this for Savings Accounts because it looks higher.
Formula: APY = (1 + r/n)n - 1 - The "Rule of 72": A quick US mental math trick. Divide 72 by your interest rate to see how many years it takes to double your money.
Example: 72 / 8% = 9 Years to double.
Frequently Asked Questions (FAQs)
What is the difference between Simple and Compound Interest?
Simple interest is calculated only on the principal amount. Compound interest is calculated on the principal plus the accumulated interest. Compound interest grows faster over time.
How often do Credit Cards compound interest?
Most US credit cards calculate interest based on your Average Daily Balance and compound it Daily. This is why credit card debt spirals out of control so quickly.
What is "Continuous Compounding"?
This is the theoretical limit where interest is calculated every infinitesimal moment. It uses Euler's number (e). The formula is A = P × ert. It is rarely used in consumer banking but common in theoretical finance.
Do I have to pay taxes on compound interest?
Yes. In the US, interest earned in a standard savings account is taxed as "Ordinary Income." You will receive a 1099-INT form from your bank if you earn more than $10.
Does the frequency (n) really matter that much?
For small amounts or short times, no. But for large mortgages or retirement funds (30+ years), the difference between Monthly and Annual compounding can be thousands of dollars.
