Compound interest means you earn or owe interest on both the original balance and previously accumulated interest. For example, if $10,000 earns 5% annually and compounds once per year, it grows to $10,500 after one year and about $11,025 after two years, assuming no withdrawals, fees, taxes, or additional deposits.
What Is Compound Interest?
Compound interest is a method of calculating interest in which previously earned interest becomes part of the balance used to calculate future interest.
This creates a compounding effect. Instead of earning interest only on the money you originally deposited, you can also earn interest on earlier interest.
The initial amount of money invested, saved, or borrowed.
The amount earned on savings or investments, or charged on debt.
The percentage used to calculate interest over a stated period.
The process of adding earned interest to the balance so future interest can be calculated on a larger amount.
How Does Compound Interest Work?
Compound interest works by repeatedly adding interest to the account balance. Each time interest is credited, the balance may become larger. The next interest calculation then uses that larger balance.
Consider an account with $10,000 earning 5% per year with annual compounding:
- Starting balance: $10,000
- After year 1: $10,500
- After year 2: $11,025
- After year 3: approximately $11,576.25
The interest earned increases slightly each year because the interest calculation is being applied to a growing balance.
Compound interest vs. simple interest
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus accumulated interest.
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest calculated on | Original principal only | Principal plus accumulated interest |
| Growth pattern | Generally linear | Generally accelerates over time |
| Long-term effect | Smaller under otherwise equal assumptions | Larger under otherwise equal assumptions |
How to Calculate Compound Interest
A common formula for annual compounding uses the starting principal, annual interest rate, and number of compounding periods.
FV = future value
PV = present value or starting principal
r = interest rate per compounding period
n = number of compounding periods
The interest earned is the future value minus the original principal.
Worked Example
Suppose you deposit $10,000 into an account that earns 5% per year, compounded annually, for 10 years.
Principal: $10,000
Annual rate: 5% or 0.05
Number of years: 10
Apply the formula:
FV = $10,000 × (1.05)10
The future value is approximately $16,288.95.
Compound interest earned: $16,288.95 − $10,000 = $6,288.95.
Estimated future value: $16,288.95Factors That Affect Compound Interest
Several inputs determine how quickly compounding changes a balance.
A larger starting amount generally produces more dollar growth when the rate and time period are otherwise equal.
Higher rates generally increase the rate at which the balance compounds.
More compounding periods give accumulated interest more opportunities to generate additional interest.
More frequent compounding can increase the effective growth rate, depending on how the quoted rate is structured.
Regular deposits can increase the amount that has an opportunity to compound over time.
Money removed from an account or costs charged against it can reduce the amount available to compound.
Common Compound Interest Mistakes
Using the wrong interest rate format.
A percentage such as 5% must usually be converted to a decimal,
such as 0.05, before using it in a formula.
Ignoring compounding frequency.
Annual, monthly, daily, and other compounding schedules can produce
different results. The rate and number of periods must match the
compounding schedule.
Confusing future value with interest earned.
Future value includes your original principal. Interest earned is
the amount above the original principal.
Ignoring fees, taxes, or withdrawals.
A theoretical compounding calculation may overstate real-world
growth if costs or withdrawals reduce the account balance.
Assuming investment returns are guaranteed.
Compound-growth examples often use a fixed rate for illustration.
Actual investment returns can vary and may be negative in some
periods.
Frequently Asked Questions
What is compound interest in simple terms?
Compound interest means interest is added to the balance, and future interest is then calculated on both the original principal and the accumulated interest.
What is the difference between compound and simple interest?
Simple interest is generally calculated only on the original principal. Compound interest is calculated on the principal plus previously accumulated interest.
Is compound interest good or bad?
It depends on whether you are earning or paying it. Compounding can help savings grow over time, but it can also make debt more expensive when unpaid interest is added to the balance.
Does compound interest work better over longer periods?
Time can have a large effect because each additional compounding period gives accumulated interest another opportunity to earn interest. The actual outcome also depends on the rate, fees, contributions, withdrawals, and other factors.
How often can interest be compounded?
Depending on the account or loan, interest may compound annually, semiannually, quarterly, monthly, daily, or on another schedule. The applicable terms should state how often compounding occurs.
Use the MoneyMetric Compound Interest Calculator
Enter your starting balance, interest rate, time period, and contributions to estimate how compound growth may change your balance over time.
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