Compound Interest Calculator
Calculate the future value of an investment over time, accounting for the power of compound interest.
Enter your initial investment amount (principal), the annual interest rate, the number of times interest is compounded per year, and the investment duration in years.
Enter Investment Details
Understanding Compound Interest & The Formula
What is Compound Interest?
Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. It's often called "interest on interest" and is the reason investments can grow exponentially over time. Unlike simple interest, which is only calculated on the principal amount, compound interest accelerates wealth creation.
The Compound Interest Formula
The future value (A) of an investment is calculated using the following formula:
A = P(1 + r/n)nt
- A = the future value of the investment/loan, including interest.
- P = the principal investment amount (the initial deposit or loan amount).
- r = the annual interest rate (in decimal form, so 5% becomes 0.05).
- n = the number of times that interest is compounded per year.
- t = the number of years the money is invested or borrowed for.
This calculator automates this formula for you, allowing you to easily see the potential growth of your money.
10 Compound Interest Examples
Click on an example to see how different scenarios play out.
Example 1: Basic Savings Goal
Scenario: Saving for a down payment.
Values: Initial: $10,000, Rate: 4% annually, Compounded: Monthly, Time: 5 years.
Calculation: A = 10000 * (1 + 0.04/12) ^ (12*5) = 10000 * (1.00333)^60 ≈ $12,210
Result: After 5 years, you'd have approximately $12,210, earning $2,210 in interest.
Example 2: Long-Term Retirement
Scenario: Starting a retirement fund early.
Values: Initial: $5,000, Rate: 7% annually, Compounded: Quarterly, Time: 30 years.
Calculation: A = 5000 * (1 + 0.07/4) ^ (4*30) = 5000 * (1.0175)^120 ≈ $40,243
Result: The initial $5,000 grows to over $40,000, showing the power of long-term compounding.
Example 3: High-Yield Savings
Scenario: Parking money in a high-yield savings account.
Values: Initial: $25,000, Rate: 5.0% annually, Compounded: Daily, Time: 2 years.
Calculation: A = 25000 * (1 + 0.05/365) ^ (365*2) ≈ $27,628
Result: Daily compounding helps maximize returns, earning over $2,600 in interest in just two years.
Example 4: Short-Term Certificate of Deposit (CD)
Scenario: A fixed-term investment.
Values: Initial: $15,000, Rate: 3.5% annually, Compounded: Semi-Annually, Time: 3 years.
Calculation: A = 15000 * (1 + 0.035/2) ^ (2*3) = 15000 * (1.0175)^6 ≈ $16,647
Result: A predictable return of over $1,600 in interest.
Example 5: The Power of Time
Scenario: A small investment left for a very long time.
Values: Initial: $1,000, Rate: 8% annually, Compounded: Annually, Time: 50 years.
Calculation: A = 1000 * (1 + 0.08/1) ^ (1*50) = 1000 * (1.08)^50 ≈ $46,902
Result: A modest $1,000 becomes nearly $47,000, demonstrating that time is the most crucial ingredient.
Example 6: Impact of a High Interest Rate
Scenario: A successful stock market investment (hypothetical).
Values: Initial: $20,000, Rate: 10% annually, Compounded: Annually, Time: 15 years.
Calculation: A = 20000 * (1 + 0.10/1) ^ (1*15) ≈ $83,545
Result: The higher rate of return leads to quadrupling the initial investment, earning over $63,000 in interest.
Example 7: Comparing Frequencies (Monthly vs Daily)
Scenario: See the effect of compounding frequency.
Values: Initial: $100,000, Rate: 6%, Time: 1 year.
Monthly: A = 100000 * (1 + 0.06/12)^12 ≈ $106,167.78
Daily: A = 100000 * (1 + 0.06/365)^365 ≈ $106,183.13
Result: Daily compounding yields about $15 more than monthly on $100k in one year. The effect is real but often subtle in the short term.
Example 8: Large Principal, Short Term
Scenario: Investing a large sum from a home sale for one year.
Values: Initial: $500,000, Rate: 4.5% annually, Compounded: Monthly, Time: 1 year.
Calculation: A = 500000 * (1 + 0.045/12) ^ 12 ≈ $522,987
Result: The large principal generates significant interest of nearly $23,000 even in a short period.
Example 9: Understanding Loan Growth
Scenario: A debt that is not being paid off (e.g., a deferred student loan).
Values: Initial: $30,000, Rate: 6.8% annually, Compounded: Daily, Time: 4 years.
Calculation: A = 30000 * (1 + 0.068/365) ^ (365*4) ≈ $39,467
Result: The loan balance grows by almost $9,500 due to compounding interest while payments are deferred.
Example 10: Saving for a Car
Scenario: Saving for a specific purchase.
Values: Initial: $15,000, Rate: 5% annually, Compounded: Monthly, Time: 3 years.
Calculation: A = 15000 * (1 + 0.05/12) ^ (12*3) ≈ $17,422
Result: The investment grows by over $2,400, getting you closer to your goal.
Frequently Asked Questions (FAQ)
1. What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal amount. Compound interest is calculated on the principal *and* the accumulated interest from previous periods, leading to exponential growth.
2. What does "compounding frequency" mean?
It's how often the interest is calculated and added to your principal. The more frequent the compounding (e.g., daily vs. annually), the faster your money grows, although the effect can be small over short periods.
3. How does this calculator work?
It uses the standard compound interest formula: A = P(1 + r/n)nt. You provide P (principal), r (rate), n (frequency), and t (time), and it solves for A (the final amount).
4. Why is starting to invest early so important?
Time (t) is an exponent in the formula, making it the most powerful factor. An investment held for 40 years will grow dramatically more than one held for 20, even with the same principal and rate.
5. Can I use this calculator for loans?
Yes. The math is the same. The "Initial Investment" would be your loan amount, and the "Final Balance" shows how much you would owe after a certain period if no payments were made.
6. Does this calculator account for regular contributions (e.g., adding $100/month)?
No. This is a lump-sum compound interest calculator. It calculates the growth of a single initial investment. A calculator for regular contributions would need to use the "Future Value of an Annuity" formula.
7. What interest rate should I use?
For savings accounts or CDs, use the stated APY. For stock market investments, use a long-term historical average (e.g., 7-10%), but remember this is an estimate and not a guarantee.
8. What if my interest is compounded continuously?
This calculator does not handle continuous compounding, which uses a different formula (A = Pert). However, daily compounding provides a very close approximation.
9. Are taxes and inflation considered in the calculation?
No. The results shown are pre-tax and do not account for inflation. The real return on your investment will be lower after accounting for taxes on the gains and the reduction in purchasing power due to inflation.
10. Why do my numbers need to be positive?
The formula is designed for growth scenarios, so the initial investment, rate, and time period must be positive numbers to produce a meaningful result.
