Compound interest calculator with compounding

Click a row to expand a year into months. CSV is provided by month — the same file shown on screen, but without the collapsed view.

How to use it

1. Enter the amount, rate, and term

   Enter the nominal annual rate from the agreement—the one printed prominently. The calculator will calculate the effective rate itself. You can set the term in years and months or with two dates. In the latter case, the number of months is calculated according to the calendar.

2. Separate capitalization and deposits

   These are two separate switches. Capitalization is how often the bank adds interest to the balance. Deposits are how often you add money. Daily interest accrual does not turn your monthly deposit into a daily one.

3. Open the advanced settings if needed

   This includes annual deposit indexation, withdrawals as a fixed amount or a percentage of accrued interest, inflation, and personal income tax with a tax-free allowance. Until you enter nonzero values, this section does not affect the result.

4. Switch “what to find” for a reverse calculation

   Enter a target amount, and the calculator will find the rate, term, or deposit amount needed to reach it. The search uses the same monthly model as the direct calculation, so the results are consistent.

5. Get the table and link

   Below the chart, you will find the yearly breakdown; each year expands into months. “Download CSV” saves the monthly table as a file. “Print” expands all years and prints the page without the form. The “Copy calculation link” button creates a URL with all fields saved in it.

The formula and what it includes

• Balance — the account balance at the start of the month: the initial amount plus everything you deposited plus interest already credited, minus withdrawals
• Month fraction — one for a full month and the remainder for the final partial month—this calculates a term of 1 year and 7 months without rounding
• Crediting — with annual capitalization, interest accumulates for twelve months in a separate line and is added to the balance in one transaction; with monthly capitalization, it is added each month; with daily capitalization, the monthly balance is multiplied by (1 + Rate ÷ 100 ÷ days in year) to the power of the number of days
• Deposit — made at the beginning or end of the period, as selected; with indexation, each following year’s deposit is multiplied by (1 + Indexation ÷ 100)
• Withdrawal — a fixed amount or a percentage of the interest accrued since the previous withdrawal; you cannot withdraw more than the remaining balance
• With simple interest — interest without capitalization: the same money, but interest is always calculated on the amount invested rather than on the amount invested plus interest
• Effective annual rate — (1 + Rate ÷ 100 ÷ m) to the power of m minus one, where m is the number of capitalizations per year: what the nominal rate becomes after capitalization
• Final amount in today’s money — the final amount divided by (1 + Inflation ÷ 100) to the power of the number of years
• Real return — (1 + effective rate) ÷ (1 + inflation) minus one—not the difference between two percentages, but their ratio
• Personal income tax — tax applies to interest credited during the calendar year above the tax-free allowance; the allowance is one million rubles multiplied by the key rate
• Doubling the amount — how long it takes the amount to double at this rate and capitalization frequency, without deposits: ln 2 ÷ (m × ln (1 + Rate ÷ 100 ÷ m))

Example breakdown: $100,000 at 10% for three years

The input data is the same as the default field values: you can calculate it mentally and confirm that the tool is telling the truth.

• Initial amount $100,000
• Rate 10% annually
• Term 3 years and 0 months
• No deposits
• Annual capitalization

1. Each month of the first year earns 100,000 × 10% ÷ 12 = $833.33. The twelve monthly amounts accumulate separately and are added to the balance at the end of the year: 100,000 + 10,000 = $110,000.

2. In the second year, interest is calculated on $110,000: $916.67 per month, or $11,000 for the year. The balance is $121,000.

3. Third year: $1,008.33 per month, or $12,100 for the year. The balance is $133,100.

4. Interest earned: 133,100 − 100,000 = $33,100.

5. With simple interest, the calculation would use $100,000 for all three years: 833.33 × 36 = $30,000.

Compound interest earned $33,100 instead of $30,000. The extra $3,100 is interest earned on the interest from the first two years. The same result comes from the classic formula 100,000 × 1.1³: for a whole-number term, the monthly model matches it.

Frequently asked questions

• How does compound interest differ from simple interest?

  What interest is calculated on. Simple interest is calculated only on the amount invested—the initial amount and each deposit. Compound interest is also calculated on interest already accrued. Over a short term, the difference is small; over a long term, it becomes the main part of the return. Both values appear side by side in the results panel, and the text below the chart explains exactly why they differ.

• What is capitalization, and why do I need to choose it?

  Capitalization is when accrued interest is added to the balance and starts earning interest itself. The more often this happens, the higher the final amount at the same nominal rate. That is why the capitalization period matters as much as the rate in the agreement.

• Why does 10% annually become 10.47% with monthly capitalization?

  Because each month earns 10 ÷ 12 = 0.8333%, and the next month is calculated from a larger amount. Over twelve months, the multiplier is 1.008333 to the twelfth power—1.1047, or 10.47% annually. This is the number shown in the “Effective annual rate” row.

• Is the deposit made at the beginning or end of the period?

  That is up to you. By default, deposits are made at the end: the deposit reaches the account after interest is credited and earns interest for one fewer period. The “at the beginning of the period” switch moves each deposit one period earlier, so the final amount is higher. Over a long term, the difference is noticeable. The monthly table shows exactly which month the money was added to the account.

• Why are deposits and capitalization separate switches?

  Because these are different things in real life. The bank credits interest on its own schedule, while you add money on yours: a paycheck once a month, a bonus once a quarter. A calculator that ties deposit frequency to capitalization would require daily deposits when interest is credited daily—something that does not happen. Here, they are separate settings, and any combination is calculated correctly because the model works month by month.

• How is personal income tax calculated, and where does the tax-free allowance come from?

  Tax applies to interest credited during the calendar year above the tax-free allowance. The allowance is one million rubles multiplied by the key rate. The calculator takes the key rate from the field next to the tax switch. The default value may become outdated, so check the Central Bank website and update it if necessary. Also note that the allowance applies to all your deposits together, while the calculator sees only one. If you have several deposits, the tax calculated for each one separately will be understated.

• Why use the Rule of 72 when the exact answer is shown next to it?

  So you can check the result without a calculator. The Rule of 72 is an approximation: divide 72 by the rate to estimate the number of years until the amount doubles. It assumes annual capitalization and is most accurate around 8% annually. The higher the rate and the more frequent the capitalization, the more it differs from the exact calculation. At 20% annually with monthly capitalization, the rule gives 3.6 years, while the actual result is about 3.5 years. Both values appear side by side so you can see the difference.

• What do “in today’s money” and “real return” mean?

  The first is the final amount adjusted to today’s prices: with 8% annual inflation, the same amount will buy about half as much in ten years. The second is the return after inflation, calculated as a ratio rather than a difference: 12% with 8% inflation gives 3.7%, not 4%. Both rows appear as soon as you enter an inflation rate.

• How does the calculator find the rate, term, or deposit amount?

  The “what to find” switch changes the unknown value. You set a target amount and everything else, and the calculator finds the missing value by repeatedly splitting the range in half using the same monthly model. It calculates the result for a trial value, compares it with the target, and narrows the range until it converges. That is why entering the answer back in standard mode produces exactly the same amount. If the target is unattainable—for example, even a 100% annual rate cannot reach it—the calculator says so instead of showing the nearest value.

• Can I use this for a loan?

  The debt grows according to the same formula, but loans are usually repaid with annuity payments, which are not included here. The calculator shows what the debt would become if nothing were paid toward it. This is useful as an upper-bound estimate, but not as a repayment schedule.

• Is any data sent anywhere?

  No. The calculation runs in your browser, and no requests are sent to the server after the page loads. A calculation link contains the same fields encoded in the page URL. It is built directly in the browser and is not sent anywhere unless you share it with someone.