Use our comprehensive Compound Interest Calculator to project the future value of your investments, determine the required initial principal, or estimate the time needed to reach your financial goals. Simply enter any three variables and the calculator will solve for the fourth.
Compound Interest Calculator
Calculated Result
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Compound Interest Calculator Formula
The standard formula for compound interest, which determines the future value of an investment, is:
Where:
- A = Future Value of the Investment/Loan
- P = Principal Investment Amount (the initial deposit or loan amount)
- r = Annual Interest Rate (as a decimal)
- n = Number of times that interest is compounded per year
- t = Number of years the money is invested or borrowed for
Variables Explained
- Present Value (P): The initial amount of money before interest is earned or compounded.
- Future Value (A): The total amount of money at the end of the investment period, including all compounded interest.
- Annual Interest Rate (r): The nominal interest rate applied to the principal over a year, expressed as a percentage.
- Time in Years (t): The total duration for which the investment will compound.
- Compounding Frequency (n): How often interest is calculated and added to the principal. More frequent compounding leads to higher returns.
Related Calculators
- Future Value Annuity Calculator
- Annual Percentage Yield (APY) Calculator
- Savings Goal Calculator
- Time to Double Money Calculator
What is Compound Interest?
Compound interest is the interest earned on both the initial principal and the interest accumulated from previous periods. It is often described as “interest on interest” and is one of the most powerful concepts in finance, enabling wealth to grow exponentially over time.
Unlike simple interest, which is only calculated on the principal amount, compounding continuously adds interest back into the principal base, leading to accelerating growth. The frequency of compounding (daily, monthly, annually) significantly impacts the final value of the investment.
How to Calculate Compound Interest (Example)
Let’s find the Future Value (A) for an initial investment (P) of $5,000, an annual rate (r) of 8%, compounded quarterly (n=4), for 10 years (t=10).
- Step 1: Convert the Rate. Convert the rate to a decimal: 8% / 100 = 0.08.
- Step 2: Plug into the Formula. $$A = 5000 \left(1 + \frac{0.08}{4}\right)^{(4 \cdot 10)}$$
- Step 3: Simplify the Parenthesis. $$A = 5000 \left(1 + 0.02\right)^{40} = 5000 \left(1.02\right)^{40}$$
- Step 4: Calculate Exponent and Final Value. $$(1.02)^{40} \approx 2.208$$ $$A = 5000 \times 2.208 = 11,040.20$$
- Result: The Future Value after 10 years is $11,040.20.
Frequently Asked Questions (FAQ)
The more frequently interest is compounded (e.g., daily vs. annually), the higher the final return will be. Daily compounding yields the highest return because the principal is adjusted more often, allowing the “interest on interest” effect to kick in sooner.
Yes, the mathematical principle is the same. For investments, compounding increases your wealth. For loans (like credit cards or mortgages), compounding increases the amount you owe, making the total cost of the loan significantly higher over time.
APR (Annual Percentage Rate) does not account for compounding. APY (Annual Percentage Yield) is the effective annual rate that takes compounding into account. APY is the more accurate measure of what you will actually earn or pay.
The standard compound interest formula calculated here assumes a single lump-sum initial deposit (P). To calculate returns with regular, recurring monthly contributions, you would need an Annuity Calculator.