Finance
Compound Interest Calculator
Project the future value of any balance — with optional monthly deposits — and watch interest earn interest. See the total earned, the effective APY, and a year-by-year growth schedule, updated live as you type.
Your plan
The principal you begin with
$
Nominal yearly rate (APR)
%
How long the money stays invested
yr
How often interest is added to the balance
optional
Money you add every period
$
Deposit at:
Future value after 20 years
$144,572.72
$86,572.72 is interest — 60% of the total
Start $10,000 Added $48,000 Interest $86,573
Total deposited
$58,000
Interest earned
$86,573
Effective APY
7.23%
How the balance grows
Year 0$144,573Year 20
Try a scenario
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The basics
What is compound interest?
Compound interest is the return you earn not just on your original money, but on the interest it has already produced. Each period the balance grows, and the next period earns on that larger base — interest on interest. Given enough time, that loop turns a steady rate into a steep curve. Two ideas do all the work.
A = P(1 + r/n)^(nt)
Interest on interest
The future value A grows from principal P at rate r, compounded n times a year for t years. Every credited return joins the principal and starts earning too.
$10,000 at 6% for 10 yrs (monthly) → $18,194
growth accelerates over time
The snowball effect
Early on, compounding looks almost like simple interest. The gap widens year after year as the interest-earning base keeps climbing, so the last decade of a long horizon usually dwarfs the first.
Year 1 adds the least; the final years add the most.
Method
How to calculate it by hand
Four steps take you from the inputs to the future value and the interest earned.
- 1
Write down the inputs
Identify the principal P, the annual rate r as a decimal, the compounding frequency n, and the time t in years.
P = 10000, r = 0.06, n = 12, t = 10 - 2
Find the rate per period
Divide the annual rate by the number of periods per year to get the growth applied each period.
r/n = 0.06 ÷ 12 = 0.005 - 3
Raise to the number of periods
Add 1, then raise it to the power of n×t — the total number of compounding periods.
(1.005)^(12 × 10) = (1.005)^120 - 4
Multiply by the principal
Multiply by P for the future value, then subtract P to isolate the interest earned.
10000 × 1.8194 = $18,194 · interest $8,194
Worked examples
See how frequency changes the result
Same $10,000 at 6% for 10 years — only the compounding frequency changes. Switch tabs to watch the formula and the answer move.
Given P = $10,000.00, r = 6%, t = 10 years, n = 12
Rate per period: 6% ÷ 12 = 0.5%
Number of periods: 12 × 10 = 120
Apply formula: A = $10,000.00 × (1 + 0.005)120
Effective annual yield (APY): 6.17%
A = $18,193.97
interest = $8,193.97Same principal, rate, and time — only the frequency changes. Notice how moving from yearly to daily compounding nudges the result up, but by far less than the rate or the years would.
Comparison
Compound vs simple interest
Simple interest pays only on the principal; compound interest pays on the growing balance. The difference is the entire reason compounding matters.
A = P(1 + rt)
Simple interest
The same fixed amount is added every year because it is always a percentage of the original P. The balance grows in a straight line.
$10,000 at 6% for 10 yrs → $16,000
A = P(1 + r/n)^(nt)
Compound interest
Interest joins the balance and earns more interest, so growth curves upward. The longer the horizon, the wider the lead over simple interest.
Same inputs, monthly → $18,194 ($2,194 more)
Where it shows up
Where compound interest matters
The same formula governs the money working for you and the debt working against you.
savings & CDs
Bank accounts
High-yield savings and certificates of deposit quote an APY — the compounded yearly return — so you can compare accounts on equal footing.
401(k) · IRA · index funds
Investing
Reinvested dividends and growth compound over decades. Starting a few years earlier often beats contributing far more money later.
cards & loans
Debt
Credit cards compound interest against you, frequently daily. The same snowball that builds savings can bury a balance you carry.
Reference
Compounding frequency at a glance
How a 6% nominal rate behaves on $10,000 over 10 years as the frequency rises — and the APY each frequency implies.
| Frequency | n / year | APY | Value after 10 yr |
|---|---|---|---|
| Annually | 1 | 6.00% | $17,908 |
| Semiannually | 2 | 6.09% | $18,061 |
| Quarterly | 4 | 6.14% | $18,140 |
| Monthly | 12 | 6.17% | $18,194 |
| Weekly | 52 | 6.18% | $18,215 |
| Daily | 365 | 6.18% | $18,220 |
Daily compounding adds only about $26 over monthly here — frequency is real but minor next to rate and time.
Quick chart
How much will $X grow to?
Pick a starting amount and a rate to see the balance at every milestone year, with interest split out — the answer to “how much is $X at Y% after N years” for hundreds of combinations.
Starting amount
Annual rate
$10,000 at 7%, compounded monthly, with no further deposits:
| Year | Interest so far | Balance |
|---|---|---|
| 1 | $723 | $10,723 |
| 2 | $1,498 | $11,498 |
| 3 | $2,329 | $12,329 |
| 4 | $3,221 | $13,221 |
| 5 | $4,176 | $14,176 |
| 10 | $10,097 | $20,097 |
| 15 | $18,489 | $28,489 |
| 20 | $30,387 | $40,387 |
| 25 | $47,254 | $57,254 |
| 30 | $71,165 | $81,165 |
Worth knowing
Rules worth remembering
A handful of shortcuts and cautions that make compound interest intuitive.
years to double ≈ 72 ÷ rate
The Rule of 72
Divide 72 by the rate for a quick estimate of how long money takes to double. At eight percent that is roughly nine years.
APY = (1 + r/n)ⁿ − 1
Effective yield
APY folds compounding into one yearly figure, so two accounts with different frequencies can be compared directly. A six percent monthly rate yields about 6.17%.
time beats timing
Start early
Because the final years grow the most, beginning sooner usually outweighs investing larger sums later. The horizon is the most powerful lever you control.
real return = rate − inflation
Mind inflation
Headline growth is nominal. Subtract your expected inflation rate before compounding to see what the balance is really worth in today's money.
deposits compound too
Contributions add up
Every recurring deposit starts its own compounding clock, so steady monthly investing often ends up larger than the lump sum you began with.
it cuts both ways
Debt compounds
The same mechanics drive credit-card balances upward. Compounding is an ally when you save and an adversary when you borrow.
FAQ
Common questions
Compound interest is interest calculated on both the original principal and the interest already added to the balance. Because each period earns a return on a slightly larger amount, the balance grows faster and faster over time — interest earning interest. That snowball is what makes long-term investing and saving so powerful.
The future value of a lump sum is A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is how many times interest compounds per year, and t is the number of years. The interest earned is A − P. When you also add regular deposits, each deposit compounds from the date it lands, so the calculator steps through period by period.
Simple interest is paid only on the original principal, so the balance grows by the same fixed amount every year. Compound interest is paid on the principal plus all the interest accumulated so far, so the growth accelerates. Over a few years the gap is small, but over decades compound interest pulls far ahead.
It helps, but less than people expect. Moving from annual to monthly or daily compounding raises the future value because interest starts earning interest sooner — but the effect is modest. On $10,000 at 6% for 10 years, yearly compounding gives about $17,908 and daily gives about $18,220. The interest rate and the time horizon do far more of the work.
APY (annual percentage yield) is the effective annual rate once compounding is taken into account: APY = (1 + r/n)^n − 1. A 6% nominal rate compounded monthly has an APY of about 6.17%. Banks advertise APY for savings because it is the true yearly return you actually earn.
Use the Rule of 72: divide 72 by the interest rate to estimate the years to double. At 6% that is about 12 years; at 8% about 9 years. It is an approximation, but it is remarkably close for the single-digit rates most savers and investors see.
Almost always, yes. Regular deposits combine your own savings with compounding on everything you have already added. Over long horizons the deposits and the interest they generate usually dwarf the starting amount — which is why automatic monthly investing builds wealth so reliably.
No — it shows nominal growth before inflation and tax. To gauge real purchasing power, subtract your expected inflation rate from the interest rate before calculating. Interest in taxable accounts may also be taxed each year, which slightly reduces the compounding effect compared with a tax-advantaged account.
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Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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