Compound Interest Calculator - Free Investment Tool
Free compound interest calculator. Enter a principal, annual interest rate, time period, and compounding frequency to see the final amount and growth chart.
Compound Interest Calculator
Documentation
What Is Compound Interest?
Compound interest is interest calculated on both a starting amount of money and the interest that amount has already earned. This is different from simple interest, which is calculated only on the original amount. Because each round of interest adds to the balance that earns the next round, compound interest makes money grow faster the longer it is left alone. The compound interest calculator on this page works out the final amount for a given starting balance, interest rate, time period, and compounding frequency.
How to Use the Compound Interest Calculator
- Enter the principal, the amount of money at the start.
- Enter the annual interest rate as a percentage, for example 5 for 5%.
- Enter the time period in years.
- Choose the compounding frequency: annually or monthly.
- Read the final amount and the growth chart, which update as soon as all fields are filled in.
Compound Interest Formula
The calculator uses this formula:
A = P (1 + r/n)^(nt)
- A is the final amount, principal plus interest.
- P is the principal, the starting amount.
- r is the annual interest rate written as a decimal (5% becomes 0.05).
- n is the number of times interest is added per year. This calculator uses n = 1 for annual compounding and n = 12 for monthly compounding.
- t is the time in years.
Some banks compound interest quarterly or daily, and in theory interest can compound continuously. This calculator only offers annual and monthly compounding, since those are the two frequencies most savings accounts and loans actually use.
How to Calculate Compound Interest
Follow these steps to work out a final amount by hand.
- Turn the interest rate into a decimal by dividing by 100.
- Pick n: use 1 for annual compounding or 12 for monthly compounding.
- Multiply n by the number of years (t) to get the total number of compounding periods.
- Divide the decimal rate by n, add 1, then raise the result to the power of nt.
- Multiply that result by the principal to get the final amount.
Example
A saver deposits $1,000 at an annual interest rate of 5%, compounded annually, for 10 years.
- r/n = 0.05 / 1 = 0.05
- nt = 1 × 10 = 10
- A = 1,000 × (1.05)^10 = $1,628.89
The account earns $628.89 in interest over 10 years.
Worked Examples
| Principal | Rate | Time | Compounding | Final amount |
|---|---|---|---|---|
| $1,000 | 5% | 10 years | Annually | $1,628.89 |
| $1,000 | 5% | 10 years | Monthly | $1,647.01 |
| $1,000 | 20% | 10 years | Annually | $6,191.74 |
| $10,000 | 7% | 30 years | Monthly | $81,164.97 |
The second row shows how compounding frequency changes the result. The same 18.12 more when interest compounds monthly instead of annually, because interest is added to the balance 12 times a year instead of once.
Compound Interest vs. Simple Interest
Simple interest is calculated only on the principal, so it grows in a straight line. Compound interest is calculated on the principal plus any interest already earned, so it grows faster over time, especially over long periods or at high rates. A loan or investment described only by its rate can still produce very different results depending on which method is used.
The Rule of 72
The Rule of 72 is a quick way to estimate how long it takes an amount to double at a given annual interest rate. Divide 72 by the interest rate to get the approximate number of years.
For example, at 6% annual interest: 72 ÷ 6 = 12 years to double. At 7%, it takes about 72 ÷ 7 ≈ 10.3 years. The rule is a rough estimate and is most accurate for rates between about 6% and 10%.
Compound Interest and Inflation
Inflation reduces what money can buy over time, so it is worth comparing an interest rate against the inflation rate. The real interest rate is the nominal (stated) interest rate minus the inflation rate. If a savings account pays 5% and inflation is 2%, the real interest rate is about 3%. If inflation is higher than the interest rate, the real interest rate is negative, meaning the money loses purchasing power even though the account balance keeps growing.
Common Uses for Compound Interest Calculations
- Savings accounts: estimate how a balance grows at a given rate.
- Investment planning: project the future value of money set aside for a goal such as retirement.
- Loans and mortgages: see how much interest adds to the amount owed over the life of a loan.
- Credit card debt: see how quickly a balance grows when only minimum payments are made.
- Retirement accounts: model how a 401(k) or similar account might grow over decades.
Frequently Asked Questions
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the principal. Compound interest is calculated on the principal and on interest already earned, so it grows faster over time.
Does this calculator support quarterly or daily compounding?
No. This calculator supports annual and monthly compounding only. Quarterly and daily compounding exist at some banks, but are not available as options here.
Can this calculator be used for loans as well as investments?
Yes. The formula works the same way whether money is growing in an investment or owed on a loan. For a loan, the final amount is the total that would be owed if no payments were made during the period.
How much does compounding frequency change the result?
More frequent compounding produces a larger final amount, but the difference is usually modest. For 16,288.95 and monthly compounding gives 181.14.
What is a realistic interest rate to use?
This depends on the account or investment. High-yield savings accounts and typical stock market index funds vary widely by year and by country, so it is best to use the actual rate stated by a bank or the historical average return of an investment.
Why does the calculator require the principal and time to be greater than zero?
A balance of zero or less has no meaningful interest to calculate, and a time period of zero or less does not describe any span of time. The interest rate may be zero, but it cannot be negative. The calculator shows an error message if the principal or time is missing, zero, or negative, or if the rate is negative.