Theme

Compound interest calculator

See how regular saving can grow over time.

  • Formula and assumptions shown
  • Table and CSV export
  • Runs in your browser

· How we check our calculators

Inputs

Changes the currency amounts are shown in. Nothing is converted.
$USD
$USD
%
years
%

Results update as you type. Rates are nominal annual rates.

Result

Ready to calculate

Calculated result—

Enter your numbers to see an estimate.

Assumptions and methodology

How it works

The calculator credits interest at the end of each modeled month. With the default monthly compounding, the monthly rate is the nominal annual rate divided by 12; for annual, semiannual, quarterly, or daily compounding it uses the equivalent monthly rate, so the starting amount grows exactly as that compounding would over each whole year. Your contribution can be added after that month's interest or at the beginning of the month before interest is applied.

Formula

Monthly rate r = i ÷ 12 with monthly compounding, or (1 + i ÷ m)^(m ÷ 12) − 1 for m compounding periods a year. After n months, FV = P × (1 + r)^n + C × ((1 + r)^n − 1) ÷ r, with the contribution term multiplied by (1 + r) for beginning-of-month deposits; if r = 0, FV = P + C × n. Today's dollars = FV ÷ (1 + inflation)^years.

The result separates your starting balance and contributions from the interest estimate so you can see what came from saving and what came from growth. Enter an optional inflation rate to also see the final balance in today's dollars. It is a planning model, not a promise of a particular account return.

Time and rate do most of the work. Each month's interest is calculated on a larger balance than the month before, so extending the term or raising the rate increases the interest share faster than it increases your contributions. Run a lower planning rate alongside your main one to see a range rather than a single number.

Read the full methodology

Assumptions

  • Rates are nominal annual percentages that stay constant for the modeled term. Monthly compounding divides the rate by 12; other frequencies use the equivalent monthly rate (1 + rate ÷ periods)^(periods ÷ 12) − 1.
  • Contributions are the same each month and are made either at the beginning or end of that month. With less frequent compounding they grow at the equivalent monthly rate; an account that credits interest only at the end of each period may pay slightly less on deposits made during it.
  • The optional today's-dollars figure divides the final balance by (1 + inflation rate)^years, using one constant annual inflation rate.
  • The estimate excludes taxes, account fees, withdrawals, changing rates, and investment volatility.
  • Balances keep full precision during calculation and are rounded only for display.

Worked example

$10,000 plus $200 a month at 5% for 10 years

With end-of-month contributions, the estimated balance after 120 months is $47,526.55: the $10,000 starting amount, $24,000 of contributions, and $13,526.55 of modeled interest. Moving the same contributions to the beginning of each month raises the estimate to $47,655.95.

Step by step

  1. Convert the rate to a monthly rate. 5% ÷ 12 = 0.4167% a month (0.0041667 as a decimal). The model applies this rate to the balance in each of the 10 × 12 = 120 months.
  2. Grow the starting amount. The monthly growth factor compounded over 120 months is 1.0041667^120 = 1.6470, so the $10,000 starting amount on its own grows to $16,470.09.
  3. Grow the monthly contributions. Each $200 deposit earns interest for the months left after it is made. Together the 120 deposits are worth $200 × (1.6470 − 1) ÷ 0.0041667 = $200 × 155.2823 = $31,056.46.
  4. Add the two parts. $16,470.09 + $31,056.46 = $47,526.55, the future balance in the example.
  5. Separate deposits from interest. Total invested is $10,000 + 120 × $200 = $34,000. Interest earned is $47,526.55 − $34,000 = $13,526.55.
  6. Move deposits to the start of each month. Each deposit then earns one extra month of interest, so the contribution part becomes $31,056.46 × 1.0041667 = $31,185.86 and the balance $47,655.95, which is $129.40 more.

How to read your result

Future balance is the modeled account value at the end of the last month, after that month’s interest and deposit. Total invested is the starting amount plus every contribution, and Interest earned is the rest. In the example, interest is $13,526.55 of the $47,526.55 balance, about 28%.

The chart plots the balance month by month, and the schedule table lists each month’s balance, interest, and contribution. The interest column rises because each month’s interest is figured on a larger balance: month 1 earns $41.67 on $10,000, while month 120 earns $196.38.

All figures are nominal dollars before taxes and account fees; enter an inflation rate to also see the final balance in today’s dollars. The Compounding menu covers accounts that compound annually, semiannually, quarterly, or daily; an account that quotes only an APY will differ slightly unless you enter its nominal rate. For a market investment, the rate stands in for an average return; actual returns vary from year to year, so the balance on any given date can sit well above or below this path.

What changes the result most

Rate
Raising the rate from 5% to 6% lifts the 10-year balance from $47,526.55 to $50,969.84, which is $3,443.29 more from the same $34,000 of deposits.
Time
Doubling the term to 20 years gives $109,333.14. Deposits double to $58,000, but interest nearly quadruples, from $13,526.55 to $51,333.14.
Monthly contribution
Raising the deposit from $200 to $300 a month adds $12,000 of deposits over 10 years and brings the balance to $63,054.78, which is $15,528.23 more than the example.
Contribution timing
Timing moves the result least here: beginning-of-month deposits add $129.40 over 10 years at 5%.

Questions

Is this an APY calculator?

No. It takes a nominal annual rate and the compounding frequency you choose (monthly by default). If your account advertises APY, the APY calculator shows the effective annual yield of a nominal rate at a chosen compounding frequency, which helps you check whether the rate you enter here matches the advertised figure.

Does contribution timing matter?

Yes. A beginning-of-month contribution receives that month's modeled interest, while an end-of-month contribution is added after interest. The difference grows with the rate and term.

Will my actual balance match this result?

Not necessarily. Actual accounts may change rates, apply fees, credit interest on a different schedule, or use different deposit timing. Use the estimate to compare a consistent set of assumptions.

How does compound interest work?

Interest is added to the balance, and later interest is calculated on that larger balance. With no deposits, $10,000 at 5% earns $41.67 in its first month, and the second month’s interest is figured on $10,041.67. Over 10 years the $10,000 grows to $16,470.09 with monthly compounding, compared with $15,000 under simple interest at the same rate.

What is the rule of 72?

It is a shortcut for doubling time: divide 72 by the annual rate. At 5%, 72 ÷ 5 = 14.4 years. With monthly compounding the exact doubling time is ln 2 ÷ (12 × ln(1 + 0.05 ÷ 12)) = 13.9 years, and the savings time calculator reports 167 months for $10,000 to reach $20,000 at 5%. The rule is an approximation that works best at moderate rates.

More in Savings & investing

Sources

These references explain the concepts behind the calculation. They do not endorse this site. Estimates leave out any cost or condition you did not enter.

Embed this calculator on your site: free, with no tracking.