Compound Interest Calculator
See how a lump sum plus regular deposits grows with daily, monthly, quarterly or annual compounding — with a year-by-year table, chart and inflation adjustment.
Compound Interest Calculator: with the default inputs, final balance is $31,998.32.
The lump sum you begin with.
The nominal (stated) annual rate.
Set to 0 for a lump sum only.
Start-of-period deposits earn one extra period of interest.
- Total contributions
- $22,000.00Starting amount plus every deposit.
- Total interest earned
- $9,998.32
- Effective annual rate (APY)
- 5.116%What the nominal rate is really worth once compounding is counted.
- Final balance in today's dollars
- —Shown when the inflation option is on.
Assumptions
- The interest rate stays constant for the whole period.
- Daily compounding uses 365 periods a year; contributions are credited at the effective rate for their own frequency.
- No taxes or fees are deducted from interest.
- Today's-dollars figures divide by (1 + inflation)^years.
| Year | Deposits | Interest this year | Total contributed | Balance |
|---|---|---|---|---|
| 1 | $1,200 | $540 | $11,200 | $11,740 |
| 2 | $1,200 | $629 | $12,400 | $13,568 |
| 3 | $1,200 | $722 | $13,600 | $15,490 |
| 4 | $1,200 | $820 | $14,800 | $17,510 |
| 5 | $1,200 | $924 | $16,000 | $19,634 |
| 6 | $1,200 | $1,032 | $17,200 | $21,867 |
| 7 | $1,200 | $1,147 | $18,400 | $24,213 |
| 8 | $1,200 | $1,267 | $19,600 | $26,680 |
| 9 | $1,200 | $1,393 | $20,800 | $29,273 |
| 10 | $1,200 | $1,526 | $22,000 | $31,998 |
How this is worked out
The formula
A = P × (1 + r/m)^(m·t) + PMT × [ (1 + i)^n − 1 ] ÷ i (× (1 + i) for start-of-period deposits) P = starting amount r = annual rate (decimal), m = compounding periods per year t = years, PMT = regular deposit i = (1 + r/m)^(m/k) − 1 = effective rate per deposit, k = deposits per year, n = k·t APY = (1 + r/m)^m − 1
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Starting amount
- The lump sum you begin with.in dollars · 0 or more · defaults to 10000
- Annual interest rate
- The nominal (stated) annual rate.a percentage · from 0 to 100 · defaults to 5
- Time
- A number.from 0 to 100 · whole numbers only · defaults to 10
- Compounding frequency
- Choose one of 4 options.Daily (365/yr) · Monthly · Quarterly · Annually
- Regular contribution
- Set to 0 for a lump sum only.in dollars · 0 or more · defaults to 100
- Contribution frequency
- Choose one of 2 options.Monthly · Annually
- Contribution timing
- Start-of-period deposits earn one extra period of interest.End of period · Start of period
- Show value in today's dollars(under More options)
- Turn this on or off.defaults to off
- Inflation rate(under More options)
- US CPI has averaged roughly 3% a year over the long run.a percentage · from 0 to 50 · defaults to 3
What you get back
- Final balancemain answer
- Total contributions
- Starting amount plus every deposit.
- Total interest earned
- Effective annual rate (APY)
- What the nominal rate is really worth once compounding is counted.
- Final balance in today's dollars
- Shown when the inflation option is on.
What this assumes
- The interest rate stays constant for the whole period.
- Daily compounding uses 365 periods a year; contributions are credited at the effective rate for their own frequency.
- No taxes or fees are deducted from interest.
- Today's-dollars figures divide by (1 + inflation)^years.
About this calculator
Compound interest is interest earned on interest. Each period the bank credits interest to your balance, and next period's interest is figured on the bigger balance. Over a few years the effect is mild; over decades it dominates — at 7% a lump sum doubles roughly every ten years without any new deposits.
How to use it
Enter your starting amount, the annual rate, how long you'll leave it, and how often the account compounds (most savings accounts compound daily or monthly; bonds and CDs often annually or semi-annually). Add a regular deposit if you'll keep contributing. Solve for answers the reverse questions: what rate or how many years gets me to $100,000? Open More options to see the ending balance in today's purchasing power.
Reading the results
- Final balance is the headline number: everything you put in plus all the interest.
- Total contributions is your own money — the starting amount plus every deposit.
- Total interest is the gap between the two. Watch how it overtakes contributions in the chart; that crossover is compounding doing the work.
- APY converts the stated rate into what you actually earn in a year. 5% compounded monthly is an APY of 5.116%; compounded daily it's 5.127%. Banks are required to quote APY, so use it to compare accounts.
Frequency matters less than you think
Going from annual to monthly compounding on 5% adds about 0.12 percentage points of yield. Going from monthly to daily adds another 0.01. The rate itself, and the time you leave the money alone, matter far more than the compounding schedule.
Caveats
The calculator assumes a constant rate. Savings rates float, and investment returns vary year to year — a 7% average with big swings ends up somewhat below a steady 7%. Interest in a taxable account is taxed as ordinary income each year, which quietly trims the compounding; retirement accounts avoid that drag. And a nominal balance that triples over 30 years buys only about 1.2× as much if inflation runs 3%, which is why the today's-dollars option exists.
Frequently asked questions
▸What is the compound interest formula?
A = P(1 + r/m)^(mt), where P is the starting amount, r the annual rate as a decimal, m the number of compounding periods per year and t the number of years. Regular deposits add a future-value-of-annuity term, PMT × ((1 + i)^n − 1) / i.
▸What's the difference between APR and APY?
APR is the simple annual rate before compounding; APY includes the effect of compounding within the year. 6% APR compounded monthly is 6.17% APY. For deposits, APY is the number that tells you what you'll actually earn.
▸Does compounding daily instead of monthly make a big difference?
Barely. On 5%, daily compounding yields 5.127% versus 5.116% monthly — about $1 a year on $10,000. Rate and time matter far more.
▸How long does it take money to double?
Divide 72 by the interest rate for a quick estimate: at 6% about 12 years, at 9% about 8 years. The exact answer is ln 2 ÷ ln(1 + r), which the Rule of 72 calculator shows alongside the estimate.
▸Why is my 'today's dollars' balance so much lower?
Because inflation erodes what each dollar buys. At 3% inflation, prices roughly double every 24 years, so a balance that doubles over that time has only kept pace.
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