Compound interest calculator

Enter a starting balance, a monthly contribution and a rate, and see what compounding does to it: the default scenario turns $58,000 of deposits into $109,333 over 20 years. The formula, every assumption and a worked example are below the worksheet.

Worksheet

Starting balance $

Monthly contribution $

Annual interest rate %

Years yrs

Compounds ▾

Balance after 20 years $109,333

You paid in: $58,000
Interest earned: $51,333
Growth multiple: 1.89×

Year-by-year schedule

Year	Paid in	Interest	Balance
1	$12,400	$567	$12,967
2	$14,800	$1,287	$16,087
3	$17,200	$2,165	$19,365
4	$19,600	$3,212	$22,812
5	$22,000	$4,435	$26,435
6	$24,400	$5,843	$30,243
7	$26,800	$7,446	$34,246
8	$29,200	$9,254	$38,454
9	$31,600	$11,277	$42,877
10	$34,000	$13,527	$47,527
11	$36,400	$16,014	$52,414
12	$38,800	$18,751	$57,551
13	$41,200	$21,751	$62,951
14	$43,600	$25,028	$68,628
15	$46,000	$28,595	$74,595
16	$48,400	$32,467	$80,867
17	$50,800	$36,660	$87,460
18	$53,200	$41,190	$94,390
19	$55,600	$46,075	$101,675
20	$58,000	$51,333	$109,333

How the formula works

Compound interest means each period's interest is added to the balance, and the next period's interest is computed on that larger balance. Two things grow side by side here: the starting balance $P$, and the stream of monthly contributions $C$. The ending balance is the sum of both:

\[ \mathrm{FV} \;=\; \underbrace{P\Bigl(1+\tfrac{r}{n}\Bigr)^{nt}}_{\text{starting balance}} \;+\; \underbrace{C\cdot\frac{(1+i)^{12t}-1}{i}}_{\text{monthly contributions}} \]

where $r$ is the annual rate as a decimal, $n$ how many times a year interest compounds, $t$ the number of years — and $i$ the effective monthly rate, which converts whatever compounding frequency your account uses into a rate that matches the monthly deposits:

\[ i \;=\; \Bigl(1+\tfrac{r}{n}\Bigr)^{n/12}-1 \]

When interest compounds monthly, $i$ is simply $r/12$. When it compounds daily or quarterly, $i$ is the monthly rate that produces exactly the same growth, so deposits and compounding stay in step whatever the account does. The calculator applies this month by month — deposits land at the end of each month — which is also why you can check any row of the schedule by hand.

What each input means

Starting balance — $P$: What is in the account today. It can be zero: the contribution stream does not need a head start, it just benefits from one.
Monthly contribution — $C$: What you add every month, assumed constant and deposited at the end of the month. If you contribute per paycheck, multiply a biweekly amount by 2.17 to get its monthly equivalent.
Annual interest rate — $r$: The quoted yearly rate. Banks advertise savings rates as APY, which already includes compounding — if you enter an APY, set the frequency to yearly and the result matches the advertised yield. For an investment return assumption, a long-run figure like 5–7% is a common starting point; nothing guarantees it.
Years — $t$: How long the money compounds. Time is the input that does the heavy lifting: doubling the rate roughly doubles the interest, but doubling the years far more than doubles it, because growth stacks on growth.
Compounding frequency — $n$: How often interest is credited: daily (365), monthly (12), quarterly (4) or yearly (1). Savings accounts usually compound daily or monthly; CDs vary. The difference between frequencies is real but small — see the questions below.

A worked example

Take the worksheet's opening numbers: $10,000 already saved, $200 added at the end of every month, 5% a year compounded monthly, for 20 years.

Compounded monthly, the effective monthly rate is $i = 0.05/12 = 0.004167$, and over 20 years there are $12t = 240$ monthly periods, so the growth factor is $(1+i)^{240} = 2.7126$. The two parts of the formula:

The starting $10,000 grows by that factor on its own: $10,000 × 2.7126 = $27,126.
The $200 monthly deposits accumulate to $200 × (2.7126 − 1) / 0.004167 = $82,207.

Together: $109,333. Of that, $58,000 is money you put in — the other $51,333 is interest, and more than half of it arrives in the final third of the timeline. That is the shape of compounding: slow, then sudden.

Fig. 1 — The worked example, month by month. The gap between the two lines is interest: $51,333 by year 20, most of it earned late.

Assumptions and limits

The rate is constant for the whole period. Real savings rates float and real investment returns swing; treat the output as a projection of an assumption, not a promise.
Contributions are constant and monthly, deposited at the end of the month. Depositing at the start of the month would earn one extra month of interest per deposit — about $343 more here.
Nothing is deducted: no taxes on the interest, no fees, no inflation. Each of those reduces the real result — the questions below put numbers on tax and inflation.
This is arithmetic, not advice. It shows what the inputs imply; it cannot know what rate you will actually get.

Questions people ask

Is the rate I enter APR or APY?

Either, if you match the frequency. An APR is the quoted nominal rate before compounding: enter it with the frequency your account actually compounds at. An APY already includes compounding: enter it with the frequency set to yearly and the growth matches the advertised yield. For savings accounts the two are close; the distinction matters more as rates rise.

Does the compounding frequency matter much?

Less than most people expect. The worked example's inputs grow to $109,484 compounded daily, $109,333 compounded monthly and $107,694 compounded yearly — a spread of about $1,790 over 20 years. The rate and the time dwarf the frequency; do not switch banks over compounding frequency alone.

How long does it take money to double?

Divide 72 by the interest rate. At 5% a balance doubles in roughly 72 / 5 ≈ 14.4 years; at 8%, about 9 years. The rule of 72 is an approximation of the exact answer ln 2 / ln(1 + r), and it is accurate to within a few months for rates under 10%.

Is the result before or after tax?

Before. Interest from savings accounts and CDs is ordinary taxable income in the year it is credited, so in a 22% bracket an account yielding 5% keeps about 3.9% after federal tax. Interest inside an IRA, 401(k) or HSA compounds without annual tax, which is why the same rate grows meaningfully faster in a sheltered account.

Does this account for inflation?

No — the result is in future dollars. To think in today's money, subtract expected inflation from the rate: 5% growth during 3% inflation is roughly a 2% real return. Run the calculator with that lower rate to see purchasing power instead of the account statement's number.