PhD in Economics, 15+ years researching long-term investment models and capital growth strategies.
Use this powerful compound interest calculator to determine the future value of an investment or loan. Simply enter the **principal amount**, **annual interest rate**, **time period**, and the **compounding frequency** to see your potential returns.
Compound Interest Calculator
Compound Interest Formula
Formula Source: Investopedia – Compound Interest
Variable Definitions:
- **A**: The **Future Value** of the investment/loan, including interest.
- **P**: The **Principal** initial amount invested or borrowed.
- **r**: The **Annual Nominal Interest Rate** (expressed as a decimal, e.g., 5% = 0.05).
- **n**: The **Number of Compounding Periods** per year (e.g., 12 for monthly).
- **t**: The **Time** in years.
Related Calculators
- Simple Interest Calculator
- Savings Goal Calculator
- Annual Percentage Yield (APY) Calculator
- Retirement Savings Calculator
What is Compound Interest?
Compound interest is the interest earned on both the initial principal and the accumulated interest from previous periods. This concept is often referred to as “interest on interest,” and it’s what makes your money grow faster over time compared to simple interest.
The power of compounding is that the base amount for calculating future interest constantly increases. For investors, this exponential growth is the key to building substantial long-term wealth. For borrowers, understanding compounding is crucial, as it can significantly increase the total cost of a loan, particularly on credit cards or high-interest debts.
How to Calculate Compound Interest (Example)
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Identify Your Variables
Suppose you invest **£5,000** (P) at an **8%** annual rate (r = 0.08), compounded **quarterly** (n = 4) for **5 years** (t).
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Plug the Values into the Formula
$$A = 5000 (1 + \frac{0.08}{4})^{(4 \times 5)}$$
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Solve for the Future Value (A)
First, simplify the inside: $1 + 0.02 = 1.02$. The exponent is $4 \times 5 = 20$.
$$A = 5000 (1.02)^{20}$$
Calculating $1.02^{20} \approx 1.4859$.
$$A = 5000 \times 1.4859 = \text{£7,429.50}$$ -
Determine Total Interest Earned
Subtract the initial principal (P) from the future value (A).
$$\text{Total Interest} = \text{£7,429.50} – \text{£5,000} = \text{£2,429.50}$$
Frequently Asked Questions (FAQ)
Yes, significantly. The more frequently interest is compounded (e.g., daily vs. annually), the greater the total future value will be, because interest starts earning interest sooner.
What is the difference between Simple and Compound Interest?Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus all the accumulated interest from previous periods, leading to exponential growth.
What is the Rule of 72?The Rule of 72 is a quick estimation tool to determine how long it will take for an investment to double. You divide 72 by the annual interest rate (without converting to a decimal) to get the approximate number of years.
Is compound interest good or bad?It is generally good when you are earning it (investments) and can be bad when you are paying it (debt/loans), as it accelerates both growth and cost.