Compound Interest Calculator
Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. Often called "interest on interest," it is one of the most powerful concepts in finance, allowing your money to grow exponentially over time rather than linearly.
Understanding compound interest is essential for making informed decisions about savings, investments, and loans. The frequency of compounding — whether daily, monthly, quarterly, or annually — directly affects how quickly your money grows. Even small differences in interest rates or compounding periods can lead to significant differences over long time horizons.
How it works
A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.
Use cases
- Planning long-term savings and retirement accounts
- Comparing investment options with different compounding frequencies
- Understanding the true cost of loans and credit card debt
- Projecting future value of regular monthly contributions
Frequently asked questions
How is compound interest calculated?
The formula is A = P × (1 + r/n)^(n×t), where P is the principal, r the annual rate, n the number of compounding periods per year, and t the time in years. For example, $1,000 at 5% per year compounded monthly for 10 years grows to 1,000 × (1 + 0.05/12)^120 ≈ $1,647. The interest earned is the final amount minus the principal.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal, so it grows linearly: I = P × r × t. Compound interest is calculated on the principal plus previously accumulated interest, so it grows exponentially. Over 10 years at 5% per year, $1,000 earns $500 with simple interest but about $629 with annual compounding.
Does the compounding frequency really matter?
Yes. The more often interest compounds, the higher the effective annual return. A nominal 5% rate yields exactly 5% with annual compounding, about 5.12% with monthly compounding, and about 5.13% with daily compounding. The difference becomes more significant with higher rates and longer time horizons.
How long does it take to double money with compound interest?
A quick estimate is the Rule of 72: divide 72 by the annual interest rate. At 8% per year, money doubles in roughly 72 / 8 = 9 years; at 6%, in about 12 years. The exact time is t = ln(2) / ln(1 + r).
How do monthly contributions affect compound growth?
Regular contributions accelerate growth significantly because each deposit starts compounding from the moment it is added. The future value of a series of monthly deposits is FV = PMT × [((1 + i)^m − 1) / i], where i is the monthly rate and m the number of months. For example, $100 per month at 0.5% monthly for 10 years accumulates to about $16,388.