Compound Interest Calculator

What this calculator answers

How much a starting amount plus regular contributions grows to after a number of years at a steady rate, how much of that is money you put in and how much is growth. It handles contributions weekly to yearly, at the start or end of each period, interest compounded daily to yearly or continuously, a time that ends partway through a year, contributions that rise each year and, if you want it, the balance in today’s dollars.

How to use it

• Initial deposit: what is in the account at the start, in dollars. 10,000, $10,000 and 10k all work. Enter 0 if you start from nothing.
• Years: how long the money grows. Decimals work: 7.5 is read as 7 years 6 months.
• Regular contribution: the amount you add each period, and how often (weekly, every 2 weeks, monthly, quarterly or yearly). The line under it shows the yearly total, which catches a yearly amount typed as monthly. Enter 0 for no contributions.
• Contribution timing: whether each contribution goes in at the end or the start of its period.
• Annual interest rate: the yearly rate your account pays, or the average return you expect from an investment, in percent. Type 6 for 6%. A negative rate, down to −50%, models a steady loss.
• Compounding: how often interest is added to the balance, as your account terms state. If you only have an APY, choose Annually (see the common mistakes below).
• Yearly increase (optional): raises every contribution by this percentage at the start of each new year, for example to match a raise.
• Inflation rate (optional): adds the balance in today’s dollars. The headline stays in future dollars.

Results update as you type. The Try buttons load the variations in the table under the worked example. The what-if tabs (Rate, Compounding and Deposit) repeat the calculation at other rates, at every compounding frequency and at other contribution amounts. To weigh two savings plans, press Save for comparison before and after a change: each saved plan shows how its balance and growth differ from the first. Continue in the Retirement Withdrawal Calculator takes the final balance over to see how long it would last.

How compound interest works

With compound interest, the interest already earned starts earning interest too. Each time interest is added to the balance, the next interest is figured on the bigger balance, so growth speeds up the longer the money stays in. With regular contributions, growth comes from two places: each contribution starts compounding from the day it goes in, and the growing balance earns more every period. In the example below, growth in the last year alone is $7,215.26, three times the $2,400.00 contributed that year.

Compound interest formula with regular contributions

The balance is the initial deposit grown for n periods plus every contribution grown from the day it was made:

$$FV = P\,(1+i)^{n} + C \times \frac{(1+i)^{n} - 1}{i} \times (1+i)^{s}$$

• $FV$ is the balance at the end.
• $P$ is the initial deposit and $C$ the contribution each period.
• $n$ is the number of contribution periods: years × contributions a year.
• $i$ is the rate per contribution period (below).
• $s$ is 0 for contributions at the end of each period and 1 at the start, because a contribution at the start earns one more period.
• At 0%, the contribution part is simply $C \times n$.

When interest compounds $m$ times a year and you contribute $p$ times a year, the annual rate $r$ is turned into the equivalent rate for one contribution period:

$$i = \left(1 + \frac{r}{m}\right)^{m/p} - 1 \qquad E = \left(1 + \frac{r}{m}\right)^{m} - 1$$

$E$ is the effective annual rate. With continuous compounding, $i = e^{r/p} - 1$ and $E = e^{r} - 1$. When $m = p$, $i$ is just $r/m$. The textbook annuity formula assumes one contribution per compounding period, so this conversion is what lets monthly contributions work with daily or annual compounding.

When contributions rise by $g$ each year, let $A_1$ be the first year’s contributions valued at the end of that year. Year $y$‘s contributions are then worth $A_1 (1+g)^{y-1}$ at the end of year $y$. Grown to the end of year $Y$ and added up, they form a geometric series:

$$A_1 \times \frac{(1+E)^{Y} - (1+g)^{Y}}{E - g}$$

Worked example: $10,000 plus $200 a month for 20 years

At 6% a year compounded monthly, with each $200 added at the end of the month:

1. Rate per month: i = 0.06 ÷ 12 = 0.005. Periods: n = 20 × 12 = 240 months.
2. Growth factor: $1.005^{240} \approx 3.310204$.
3. Initial deposit: $10,000 × 3.310204 = $33,102.04.
4. Contributions: $200 × (3.310204 − 1) ÷ 0.005 = $200 × 462.0409 = $92,408.18.
5. Balance: $33,102.04 + $92,408.18 = $125,510.22.
6. You put in $10,000 + 240 × $200 = $58,000.00, so growth added $67,510.22.

The effective annual rate is $1.005^{12} - 1$ = 6.1678%. Growth passes the total you put in during year 18. In a spreadsheet, =FV(6%/12, 240, -200, -10000, 0) gives the same balance.

Each Try button changes one thing from this example:

Raising the $200 by 3% every year instead (type 3 in Yearly increase) gives $150,242.94 from $74,488.90 put in; the last year’s contributions are $350.70 a month.

Does compounding daily vs. monthly make a difference?

Yes, but less than the rate or the time. For the example, only the compounding changes:

Daily compounding adds $255.09 over monthly on these numbers; one percentage point more rate adds $19,062.50 ($144,572.72 at 7%). The gains shrink as compounding gets more frequent, and continuous compounding is the limit. The Compounding tab under the result shows these balances for your own numbers.

Contributions at the start vs. end of each period

A contribution at the start of a period earns one more period of growth than the same contribution at the end, so the contribution part is multiplied by (1 + i). In the example, contributing on the first of each month instead of the last gives $125,972.26, which is $462.04 more: $92,408.18 × 0.005. The initial deposit is the same either way.

If the time ends partway through a period, contributions are made on every scheduled date inside it. For 2.3 years of monthly contributions (27.6 months), that is 27 contributions at the end of each month or 28 at the start; the last 0.6 of a month still earns growth at the same rate.

How long does it take to double your money?

A single deposit doubles in ln 2 ÷ ln(1 + E) years at an effective annual rate E. The rule of 72 estimates it as 72 ÷ the rate in percent, which is close for everyday rates:

At 6% compounded monthly, as in the example, the exact time is 11.58 years. The Time to double figure shows both for your rate.

Compound vs. simple interest

Simple interest is paid on the original deposit only; compound interest is also paid on interest already added. $10,000 at 6% for 20 years reaches $22,000.00 with simple interest, $32,071.35 compounded annually and $33,102.04 compounded monthly. With no contributions, the calculator shows the simple-interest figure next to your result.

Reading the result

• The headline is the balance at the end, with what you put in and what growth added.
• You put in is the initial deposit plus every contribution. Growth is the rest; at a negative rate it is a loss.
• Effective annual rate is the growth over one year once compounding is counted, with the rate per contribution period used in the steps.
• Time to double is for a single deposit at your rate, with the rule-of-72 estimate.
• Contributing at the start (or at the end) repeats the calculation with the other timing. With no contributions and a rate of 0% or more, this figure compares simple interest instead.
• Growth in year 20 (your last year), or In today’s dollars when you enter an inflation rate, shows how fast the balance is growing at the end, or what it would buy at today’s prices.
• The balance table lists each year’s start balance, contributions, growth and end balance and downloads as a CSV file; a second tab lists every month (or week or quarter). A part year at the end says how long it is.
• The chart stacks what you put in and the growth for each year; its Chart data table lists the numbers.
• The what-if tabs repeat the calculation at rates 1 and 2 points either side of yours, at every compounding frequency and at other contribution amounts, with the change from your result.

What this calculator assumes

• The rate stays the same for the whole time. For an investment, the result is what a steady average return would give, not a forecast.
• Contributions are the same amount every time, or rise once a year by the percentage you enter.
• Money grows at the equivalent rate per contribution period from the day it goes in. Accounts differ in how they credit interest on money added between compounding dates.
• A year is 52 weeks (26 two-week periods), and daily compounding uses 365 days.
• There are no taxes, fees or withdrawals. Amounts are in future dollars unless you enter an inflation rate.
• The balance is an educational projection, not financial advice or a promise of what any account or fund will pay.

Common mistakes

• Entering an APY with monthly or daily compounding. An APY already includes compounding, while an account’s interest rate does not. Enter an APY with annual compounding, or enter the interest rate with the compounding the account states. A 6% APY compounded monthly again would overstate the balance.
• Typing the rate as a decimal. The field is in percent, so 0.06 means 0.06%. The calculator asks whether you meant 6%.
• Using A = P(1 + r/n)^(nt) for a savings plan. That formula grows one deposit. Regular contributions need the annuity part of the formula, and the textbook version only fits when you contribute once per compounding period.
• A yearly amount with a monthly frequency. $2,400 a year typed as a monthly contribution is twelve times too much. Check the yearly total shown under the field.
• Comparing a future balance with today’s prices. $125,510.22 in 20 years buys less than $125,510.22 today. Enter an inflation rate to see the balance in today’s dollars.
• Treating the growth as certain. A savings account’s rate can change, and investment returns go up and down. Test a lower rate in the what-if table before relying on a figure.