Compound interest calculator
Enter an initial deposit, an optional regular contribution, a rate and how often it compounds. Get the final balance, total interest, effective annual yield, a year-by-year table and a growth chart -- all computed in your browser.
Start = deposited before that period's interest; end = after.
Optional: contribution increase and inflation
Steps your contribution up once per year, e.g. an annual raise.
Adds a second, inflation-adjusted balance in today's dollars.
Final balance
$50,969.84
Total contributions
$24,000.00
+ $10,000 initial
Total interest
$16,969.84
Effective annual yield (APY)
6.17%
vs. 6% nominal
Balance over time
How compound interest is calculated
Compound interest is interest paid on both the original amount and on interest already earned. The closed-form formula for a lump sum, no contributions, is:
A = P × (1 + r/n)n×t
where A is the final balance, P the principal, r the nominal annual rate (as a decimal), n the number of times it compounds per year, and t the number of years. As n grows without bound, that formula converges to continuous compounding:
A = P × er×t
With a regular contribution of PMT added every period at the same rate, the contributions themselves grow like an annuity. Added at the end of each period (interest starts the following period):
FVcontrib = PMT × [((1 + i)N − 1) / i]
where i is the periodic rate and N the number of contribution periods. Added at the start of each period instead, every contribution gets one extra period of growth, so the total is that same formula multiplied by (1 + i). The calculator adds this contribution growth to the lump-sum growth above to get the final balance.
Annual Percentage Yield (APY) restates any nominal rate and compounding frequency as the equivalent one-year return: APY = (1 + r/n)n − 1, or er − 1 for continuous compounding. It's the number to compare when two accounts quote rates at different compounding frequencies.
Worked example
The calculator's own defaults: $10,000 initial deposit, $200 contributed at the end of every month, a 6% nominal annual rate compounding monthly, over 10 years.
| Growth of the $10,000 initial deposit alone | $18,193.97 |
| Growth of the $200/month contributions | $32,775.87 |
| Final balance | $50,969.84 |
| Total contributed over 10 years | $34,000.00 |
| Total interest earned | $16,969.84 |
At 6% compounded monthly, the effective annual yield is 6.1678% -- slightly above the 6% nominal rate, because interest earned in earlier months itself earns interest in later months. Plug the same four numbers into the calculator above and it lands on the same balance to the penny; that reconciliation is checked in the site's own test suite, not just written here.
Compound vs. simple interest
Simple interest only ever applies to the original principal: A = P × (1 + r×t). Compound interest applies to principal plus all interest earned so far. The two agree exactly at the one-year mark and diverge further every year after that. $10,000 at 6%, annual compounding, no contributions:
| Years | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 | $10,600 | $10,600 | $0 |
| 5 | $13,000 | $13,382 | $382 |
| 10 | $16,000 | $17,908 | $1,908 |
| 20 | $22,000 | $32,071 | $10,071 |
| 30 | $28,000 | $57,435 | $29,435 |
How much does compounding frequency matter?
Same $10,000, same 6% nominal rate, same 10 years -- only how often it compounds changes:
| Frequency | Effective yield (APY) | Balance after 10 years |
|---|---|---|
| Daily | 6.1831% | $18,220.29 |
| Monthly | 6.1678% | $18,193.97 |
| Quarterly | 6.1364% | $18,140.18 |
| Semi-annually | 6.0900% | $18,061.11 |
| Annually | 6.0000% | $17,908.48 |
| Continuously | 6.1837% | $18,221.19 |
Going from annual to daily compounding is worth about $312 here; going from daily to continuous is worth about $0.90. Frequency matters far less than rate or time.
The Rule of 72
A quick mental shortcut for how long money takes to double at a given annual rate: divide 72 by the rate. It's an approximation of the exact doubling time, ln(2) / ln(1 + r) for annual compounding -- close in the range most savings and investment rates fall in, less accurate at very high or very low rates.
| Annual rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 4% | 18.0 yrs | 17.7 yrs |
| 6% | 12.0 yrs | 11.9 yrs |
| 8% | 9.0 yrs | 9.0 yrs |
| 10% | 7.2 yrs | 7.3 yrs |
| 12% | 6.0 yrs | 6.1 yrs |
Frequently Asked Questions
Does it matter if interest compounds daily or monthly?
Less than most people expect. At 6% on $10,000 for 10 years, daily compounding gives $18,220.29 and monthly gives $18,193.97 -- a difference of about $26.32, well under 1%. The frequency table below shows every option side by side. What actually moves the number is the rate and the time, not how finely a given rate is sliced.
What's the difference between APY and APR?
APR (annual percentage rate) is the nominal rate before compounding is applied -- what you'd multiply by the balance once a year if interest were simple. APY (annual percentage yield) is the actual one-year return once compounding is applied, and it's always equal to or higher than the APR for a positive rate. Banks are required to advertise savings and CD rates as APY; loans are usually quoted as APR. This calculator's "Annual interest rate" field is the nominal rate -- the APY box shows what that rate actually earns once your chosen compounding frequency is applied.
Does it matter if I contribute at the start or end of the month?
Yes, a little, and it compounds. A contribution made at the start of a period earns interest for that period; one made at the end doesn't, so start-of-period deposits finish slightly ahead over many periods. On the tool's own defaults, switching contribution timing from end to start changes the 10-year total by exactly one month's interest rate applied to the grown contribution stream (on the defaults, $32,775.87 × 0.5% = $163.88) -- small per period, but it's free money for changing nothing about how much you save, only when in the month you move it.
Does this account for taxes or inflation?
Not by default, and that matters. In a taxable account, interest is usually taxed as it's earned (check your own bracket and account type), which this tool doesn't model -- the number shown is gross, before tax. It does have an optional inflation field: turn it on and the tool also shows the final balance in today's purchasing power, which is normally a smaller, more honest number over long horizons than the raw dollar total.
Why does my bank's number differ from this calculator?
A few common reasons: your bank may compound daily but only credit (post) interest monthly or quarterly, which changes the compounding math slightly from a pure daily model; promotional or tiered rates change partway through the term; deposits and withdrawals during the term shift the base the interest is earned on; and some accounts use a 360-day, not 365-day, year for daily interest. This tool assumes a constant rate and constant contribution schedule for the whole term, which is the standard simplification every general-purpose calculator makes.
Is a higher compounding frequency always better?
For the saver, yes, but with fast-diminishing returns -- see the frequency table below, where daily and continuous compounding are only fractions of a percent apart in APY. Past monthly, the difference is usually not worth choosing an account over. It matters more when comparing rates already quoted at different compounding frequencies, which is what the APY conversion above is for: it puts any nominal rate and frequency on the same one-year footing.
What is the Rule of 72 actually good for?
A fast mental estimate of how long money takes to double at a given annual rate: divide 72 by the rate. It's a genuine approximation, not exact math -- see the table and caveat below -- but it's close enough for a back-of-envelope comparison between two rates without reaching for a calculator.
Can I use this for a loan instead of savings?
The compounding math is the same in both directions, but this tool is built and worded for the saver's side (a deposit growing) -- final balance, contributions in, interest earned. For a loan you're paying down, an amortization calculator (which also subtracts a payment against principal) is the right tool, not this one.
Figures on this page are estimates for a constant rate and a constant contribution schedule, for general education, not investment, tax or financial advice. Real accounts vary rates, may tax interest as it's earned, and may compound and credit on different schedules than modeled here -- see the FAQ above and the Terms.
A few related decisions this tool doesn't make for you. Whether a Roth or traditional account suits your tax situation is its own question -- VersusMath's Roth vs. traditional comparison lays out the trade-off side by side. If the money you're growing here is savings toward a house, a 15- vs. 30-year mortgage changes the total interest on the other side of the ledger, also on VersusMath. And if you're using the "annual contribution increase" field above to model a raise going straight into this contribution, WageSums's raise calculator turns a percent or dollar raise into the new paycheck number first.
Coming later
- Compound Interest Formula -- the algebra behind A = P(1+r/n)ⁿᵗ, solved for each variable.
- Compounding Calculator -- compare compounding frequencies side by side at a glance.
- Daily Compound Interest Calculator -- day-by-day accrual, the way many high-yield savings accounts actually credit interest.
- Compound Growth Calculator -- the same math applied beyond interest-bearing accounts.
- 401(k) Compound Interest Calculator -- payroll contributions, employer match, and a multi-decade horizon.
- CD Monthly Interest Calculator -- fixed-term certificates of deposit with monthly crediting.
See About for why this site launches as one calculator.