Money
Compound Interest: Formula, Examples And How It Works
Last updated: October 2026
Written by Jessica Hill
Compound interest is interest earned on both your original money and the interest it has already earned. The formula is A = P(1 + r/n)^(nt), where P is the starting amount, r is the yearly rate, n is how many times per year interest compounds, and t is the number of years. Over time, your balance grows faster and faster.
For example, $10,000 at 5% compounded yearly grows to about $43,219 in 30 years. With simple interest, it would reach only $25,000. If you want to run your own numbers, the compound interest calculator does the math instantly.
This guide is for education only and is not financial advice. Rates in the examples are hypothetical. Talk to a licensed financial professional before making investment or borrowing decisions.
What Is Compound Interest?
Compound interest is "interest on interest." Each time interest is added to your balance, the next round of interest is calculated on that larger balance.
Here is $1,000 earning 5% per year, compounded once a year:
| Year | Starting balance | Interest earned (5%) | Ending balance |
|---|---|---|---|
| 1 | $1,000.00 | $50.00 | $1,050.00 |
| 2 | $1,050.00 | $52.50 | $1,102.50 |
| 3 | $1,102.50 | $55.13 | $1,157.63 |
| 4 | $1,157.63 | $57.88 | $1,215.51 |
| 5 | $1,215.51 | $60.78 | $1,276.28 |
Notice that the interest grows every year, even though the rate stays at 5%. In year 1 you earn $50. By year 5 you earn $60.78, because the interest from earlier years is now earning interest too.
Compound Interest Vs Simple Interest
Simple interest is paid only on the original amount. Compound interest is paid on the original amount plus all the interest added so far. The gap between them starts small and becomes huge over long periods.
| Simple interest | Compound interest | |
|---|---|---|
| Interest is based on | The original amount only | The original amount plus earned interest |
| Formula | A = P(1 + rt) | A = P(1 + r/n)^(nt) |
| Growth pattern | Straight line | Curve that gets steeper |
| $10,000 at 5% for 30 years | $25,000 | $43,219 (compounded yearly) |
| Common uses | Some car loans, short-term loans, many federal student loans | Savings accounts, CDs, investments, credit cards |
In this example, compounding adds more than $18,000 compared with simple interest, with no extra money put in. You can compare the two side by side with the simple interest calculator.
The Compound Interest Formula
The compound interest formula finds the final balance after a set number of years. Each letter stands for one input.
A = P(1 + r/n)^(nt)
| Letter | Meaning | Example |
|---|---|---|
| A | Final amount (principal plus interest) | What you solve for |
| P | Principal, the starting amount | $5,000 |
| r | Annual interest rate as a decimal | 4% = 0.04 |
| n | Number of times interest compounds per year | 12 for monthly |
| t | Number of years | 10 |
To find only the interest earned, subtract the principal: interest = A – P.
How To Use The Formula Step By Step
Example: $5,000 at 4% compounded monthly for 10 years
- Convert the rate to a decimal: 4% = 0.04
- Divide by the compounding periods: 0.04 ÷ 12 ≈ 0.003333
- Add 1: 1.003333
- Find the total number of periods: 12 × 10 = 120
- Raise to that power: 1.003333^120 ≈ 1.4908
- Multiply by the principal: 7,454.17**
- Interest earned: $7,454.17 – 2,454.17**
Step 5 is the only hard part by hand. An exponent calculator handles the power, or any scientific calculator with a ^ or yˣ key.
Example: $1,000 At 6% Compounded Daily For 2 Years
This is one of the most common compound interest questions.
- P = 1,000, r = 0.06, n = 365, t = 2
- A = 1,000 × (1 + 0.06/365)^(365 × 2)
- A = 1,000 × (1.000164)^730
- A ≈ $1,127.49
The interest earned is about $127.49. With yearly compounding, the same deposit would reach $1,123.60, so daily compounding adds about $3.89 over two years.
Compound Interest With Regular Deposits
Most people do not deposit money once and walk away. They add money every month. To include regular deposits, you add a second part to the formula.
A = P(1 + i)^N + PMT × [((1 + i)^N – 1) ÷ i]
- i = rate per period (r ÷ n)
- N = total number of periods (n × t)
- PMT = the amount you add each period, at the end of the period
Example: start with $5,000, add $100 a month, at 4% compounded monthly for 10 years
- i = 0.04 ÷ 12 ≈ 0.003333, and N = 120
- Growth of the starting $5,000: 5,000 × 1.4908 ≈ $7,454.16
- Growth of the monthly deposits: 100 × [(1.4908 – 1) ÷ 0.003333] ≈ $14,724.98
- Total: $22,179.14
You put in 5,000 plus 120 deposits of $100), so about $5,179 came from interest.
How To Calculate Compound Interest In Excel Or Google Sheets
Spreadsheets have a built-in FV (future value) function that does the whole formula in one cell. The basic layout is:
=FV(rate per period, number of periods, payment per period, starting amount)
For the example above, type:
=FV(0.04/12, 120, -100, -5000)
The result is $22,179.14. The payment and starting amount are entered as negative numbers because they are money leaving your pocket, and FV returns the money coming back to you. Leave the payment as 0 if you are not adding deposits.
How Compounding Frequency Changes The Result
The more often interest compounds, the more you earn, but the extra gain gets smaller with each step up. The biggest jump comes from moving from yearly to quarterly or monthly.
$10,000 at 5% for 30 years:
| Compounding | n | Final balance | Gain over yearly |
|---|---|---|---|
| Yearly | 1 | $43,219.42 | |
| Quarterly | 4 | $44,402.13 | +$1,182.71 |
| Monthly | 12 | $44,677.44 | +$1,458.02 |
| Daily | 365 | $44,812.29 | +$1,592.87 |
| Continuously | $44,816.89 | +$1,597.47 |
Going from daily to continuous compounding adds less than $5 over 30 years. In practice, the interest rate and the time your money stays invested matter far more than the compounding schedule.
Continuous Compounding
Continuous compounding is the limit you reach if interest were added every instant. It uses the number e (about 2.71828) and a simpler formula:
A = Pe^(rt)
For $10,000 at 5% for 30 years: A = 10,000 × e^(1.5) ≈ $44,816.89. It is used mostly in finance math and economics classes. Most bank accounts compound daily or monthly.
APY Vs APR: How Banks Show Compound Interest
APY (annual percentage yield) shows what you actually earn in a year once compounding is included. APR (annual percentage rate) is the yearly rate before compounding. When interest compounds more than once a year, the APY is always higher than the stated rate.
APY = (1 + r/n)^n – 1
| Stated rate | Compounding | APY |
|---|---|---|
| 5% | Yearly | 5.00% |
| 5% | Quarterly | 5.09% |
| 5% | Monthly | 5.12% |
| 5% | Daily | 5.13% |
Under the federal Truth in Savings rules (Regulation DD), banks must give you the APY for interest-bearing deposit accounts, along with the interest rate, before you open the account. That makes APY the fair number to use when comparing savings accounts or CDs. The Federal Reserve defines it as a rate "reflecting the total amount of interest paid on an account."
For loans and credit cards, lenders usually advertise the APR. Remember that the APR does not show the full effect of compounding on what you owe.
The Rule Of 72: A Quick Doubling Shortcut
The Rule of 72 estimates how many years it takes for money to double with compound interest. Divide 72 by the yearly interest rate (as a whole number).
Years to double ≈ 72 ÷ interest rate
| Rate | Rule of 72 estimate | Exact answer |
|---|---|---|
| 3% | 24 years | 23.4 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
The rule works best for rates between about 6% and 10%. It also works backward: if you want money to double in 8 years, you need a rate of about 72 ÷ 8 = 9%. It works for debt too. At 24% APR, an unpaid credit card balance doubles in about 72 ÷ 24 = 3 years. The exact figure with daily compounding is about 2.9 years.
To find the exact doubling time, solve 2 = (1 + r)^t with logarithms: t = log(2) ÷ log(1 + r). A log calculator makes this quick.
Why Time Matters Most: Starting Early
With compound interest, the number of years your money grows matters more than almost anything else. Money invested earlier has more time to earn interest on its interest.
Example (hypothetical 7% yearly return, compounded monthly): two people each invest $200 a month until age 65.
| Starts at 25 | Starts at 35 | |
|---|---|---|
| Years investing | 40 | 30 |
| Total contributed | $96,000 | $72,000 |
| Balance at 65 | About $525,000 | About $244,000 |
| Growth from interest | About $429,000 | About $172,000 |
The early starter put in only $24,000 more, but ended up with more than twice as much. Those extra 10 years let compounding do most of the work.
The 7% rate here is for illustration only. Real investments can rise and fall, and past returns do not guarantee future results. The SEC's investor education site, Investor.gov, has a free compound interest calculator for testing your own scenarios.
How A Single Deposit Grows Over Decades
You can see the same effect with one deposit and no added contributions. Here is $10,000 at a hypothetical 7% per year, compounded yearly:
| Years | Balance |
|---|---|
| 10 | $19,672 |
| 20 | $38,697 |
| 30 | $76,123 |
The balance roughly doubles every 10 years, matching the Rule of 72 (72 ÷ 7 ≈ 10.3). Each decade adds more dollars than the one before it.
Compound Interest On Debt
Compound interest works against you when you borrow. Unpaid interest gets added to your balance, and then you pay interest on that interest too.
Credit Cards
According to the Consumer Financial Protection Bureau, many credit card issuers use a daily periodic rate, usually the APR divided by 360 or 365. Interest is added to your balance each day, so it compounds daily.
Example: a $5,000 balance at 24% APR with no payments at all for one year.
- Compounded daily: about $6,355.74
- That is about $1,356 in interest, more than the $1,200 you would expect from a flat 24%.
Paying your full statement balance by the due date usually avoids interest on new purchases. Carrying a balance is where compounding gets expensive.
Student Loans And Other Loans
Not every loan compounds. Many federal student loans charge simple daily interest, figured on the unpaid principal. But if unpaid interest is added to the principal, called capitalization, future interest is charged on the bigger balance. This often happens after a deferment ends.
Mortgages and most car loans also charge interest on the remaining balance, but because each monthly payment covers the interest due, the interest usually does not pile up on itself the way it does on an unpaid credit card.
How To Make Compound Interest Work For You
The same four inputs in the formula show you what you can control: the principal, the rate, the compounding frequency and the time.
| Lever | What to do | Why it helps |
|---|---|---|
| Time (t) | Start saving as early as you can | More years means more interest on interest |
| Principal (P) | Add money regularly, even small amounts | Each deposit starts its own compounding |
| Rate (r) | Compare APYs, not just advertised rates | A higher APY grows your money faster |
| Reinvestment | Leave interest and dividends in the account | Withdrawing interest stops it from compounding |
| Debt | Pay off high-APR balances first | Compounding debt can outpace savings growth |
Watch out for fees and inflation too. A 1% yearly fee or a high inflation rate can eat away much of the benefit of compounding over long periods. A percentage calculator helps you see what a fee costs on your balance.
Common Compound Interest Mistakes
Most compound interest mistakes come from mixing up rates and periods in the formula.
| Mistake | Fix |
|---|---|
| Using 5 instead of 0.05 for the rate | Always convert the percent to a decimal |
| Forgetting to divide the rate by n | Use r/n, the rate per period |
| Using t instead of nt for the exponent | The exponent is the total number of periods |
| Treating the final amount as the interest | Interest = A – P |
| Comparing an APR on one account to an APY on another | Compare APY to APY |
| Assuming investment returns are fixed | Real returns vary; use a range of rates when planning |
Summary
Compound interest is interest on both your principal and past interest, calculated with A = P(1 + r/n)^(nt). The longer your money compounds, the faster it grows, and more frequent compounding adds a little extra. APY shows the true yearly rate after compounding, and the Rule of 72 estimates doubling time.
The same math makes unpaid debt grow, especially on credit cards that compound daily. Start saving early, compare APYs, reinvest earnings, and pay down high-interest debt first.
Next step: plug your own savings goal into the compound interest calculator to see how different rates and time frames change the result.
Frequently Asked Questions
What is compound interest in simple terms?
Compound interest means your money earns interest, and then that interest earns interest too. Think of a snowball rolling downhill. It starts small, but as it picks up more snow, it grows faster. In a savings account, each interest payment makes your balance bigger, so the next interest payment is bigger as well.
How often is interest compounded on a savings account?
It depends on the bank. Savings accounts commonly compound daily or monthly and credit the interest to your account monthly or quarterly. The account disclosure explains the schedule and must show the APY. When comparing accounts, focus on the APY, because it already includes the effect of compounding. A daily-compounded account and a monthly one with the same APY will earn the same amount.
Can compound interest make you rich?
Compound interest can turn regular saving into a large balance over many decades, but it is not a shortcut. The results depend on how much you save, the rate you earn, how long you stay invested, and fees and taxes. Investments that offer higher potential returns also carry more risk. Small, steady contributions over a long time are where compounding helps most.
Is compound interest good or bad?
Compound interest is good when you are earning it and bad when you are paying it. On savings and investments, it helps your money grow faster over time. On credit card debt or loans where unpaid interest is added to the balance, it makes what you owe grow faster. The same formula applies either way, which is why paying off high-interest debt is often a smart first step.
What is the difference between interest rate and APY?
The interest rate is the yearly rate before compounding, while APY is the rate after compounding is counted. For example, a 5% rate compounded monthly gives an APY of about 5.12%. If interest compounds only once a year, the two numbers are the same. Banks must show the APY on deposit accounts, so it is the best number to use when comparing them.
How do you calculate compound interest monthly?
To calculate monthly compound interest, use A = P(1 + r/12)^(12t). Divide the yearly rate by 12 to get the monthly rate, and multiply the years by 12 to get the number of months. For $1,000 at 6% for 1 year: 1,000 × (1.005)^12 ≈ $1,061.68. The interest earned is about $61.68.
Try it with your own numbers
Use a free CalcSolver tool to check the examples in this guide.