Compound Interest Calculator
Calculate compound interest and see how your money grows over time. Enter principal, interest rate, time period, and compounding frequency to see your investment's future value.
Result
- Principal
- $0.00
- Interest Rate
- 0% per year
- Time Period
- 0 years
- Compounding
- N/A
- Total Interest Earned
- $0.00
- Total Amount
- $0.00
Formula & Guide
Formula
A
Compound Interest
A = P(1 + r/n)^(nt)
Future Value with Compound Interest
I
Total Interest
I = A - P
Interest = Final Amount - Principal
Formula Variables
A
Amount
The future value including principal and interest
P
Principal
The initial amount of money invested or borrowed
r
Rate
Annual interest rate (as a decimal, e.g., 5% = 0.05)
n
Frequency
Number of times interest compounds per year
t
Time
Time period in years
Example Scenario
Principal
$10,000
Interest Rate
8%
(annual)
Time Period
5 years
Compounding
Monthly (12/year)
1
Identify Variables
- P = $10,000
- r = 8% = 0.08
- n = 12 (monthly)
- t = 5 years
2
Apply the Formula
- A = P(1 + r/n)^(nt)
- A = $10,000 × (1 + 0.08/12)^(12×5)
- A = $10,000 × (1.00667)^60
3
Calculate Total Interest
- I = A - P
- I = $14,898.46 - $10,000
Compounding Frequency Comparison
Annual Compounding
Principal: $10,000
Rate: 8% per year
Time: 5 years
Compounding: Annually (n=1)
Final Amount
$10,000 × (1.08)^5 = $14,693.28
Interest Earned
$4,693.28
Daily Compounding
Principal: $10,000
Rate: 8% per year
Time: 5 years
Compounding: Daily (n=365)
Final Amount
$10,000 × (1.000219)^1825 = $14,918.25
Interest Earned
$4,918.25 (+$224.97 vs annual)
Characteristics of Compound Interest
Exponential Growth
Unlike simple interest, compound interest grows exponentially. The longer you invest, the faster your money grows.
Time is Key
Starting early makes a huge difference. Due to compounding, even small amounts invested early can outgrow larger amounts invested later.
Frequency Matters
More frequent compounding yields higher returns. Daily compounding earns more than annual compounding at the same rate.
Power of Reinvestment
Compound interest automatically reinvests your earnings. Each period's interest becomes part of the principal for the next period.
Important Notes
- Compound interest is calculated on both principal and accumulated interest. This creates exponential growth over time.
- Higher compounding frequency means more interest earned. Daily compounding earns more than monthly, which earns more than annual.
- The Rule of 72: Divide 72 by the interest rate to estimate how many years it takes to double your money.
- Compound interest works against you on debt. Credit card interest compounds, causing debt to grow quickly if unpaid.
Frequently Asked Questions
Find answers to common questions about compound interest.
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. This means your money grows faster over time as you earn 'interest on interest'. For example, if you invest $1,000 at 10% annual compound interest, after year 1 you have $1,100. In year 2, you earn 10% on $1,100, giving you $1,210.
The more frequently interest compounds, the more you earn. Annual compounding means interest is added once per year. Monthly compounding adds interest 12 times per year, so you earn interest on a slightly larger balance each month. Daily compounding adds interest 365 times per year. The difference becomes more significant with larger amounts and longer time periods.
APR (Annual Percentage Rate) is the simple interest rate without compounding. APY (Annual Percentage Yield) includes the effect of compounding and shows your actual annual return. For example, 12% APR with monthly compounding equals approximately 12.68% APY. APY is always equal to or higher than APR.
Simple interest is calculated only on the principal amount, so interest remains constant each period. Compound interest is calculated on principal plus accumulated interest, so it grows exponentially. Over time, compound interest generates significantly more returns than simple interest.
The Rule of 72 is a quick way to estimate how long it takes for an investment to double. Divide 72 by the annual interest rate to get the approximate years. For example, at 8% annual interest, your money doubles in about 72 ÷ 8 = 9 years. This rule works best for rates between 6% and 10%.
Yes, compound interest also applies to debt. Credit card debt, loans, and mortgages often compound, meaning you pay interest on accumulated interest. This can make debt grow quickly if not managed. Understanding compound interest helps you both grow wealth and manage debt effectively.