Compound Interest Calculator
Compound interest adds accrued interest back to the principal, so that interest starts earning interest of its own. The calculator shows how far a given amount will grow at a chosen rate, term and capitalisation frequency. It is the core tool for planning long-term investments and savings. Below are the formula with each variable explained, a worked example with real numbers, and the boundaries of the model.
Formula and explanation
A = P · (1 + r/n)n·t
where: P = principal, r = annual interest rate, n = number of capitalizations per year (12 for monthly, 4 for quarterly, 1 for annual), t = term in years, A = final amount.
With compound interest, the accrued interest is added to the principal and also starts earning interest — the so-called "interest on interest" effect. The more often interest is capitalized, the faster the investment grows. This calculator is a basic tool for planning long-term investments and savings.
Methodology
What the compound interest calculator works out
With compound interest, accrued interest is not paid out but added to the principal, so from the next period onwards it earns interest of its own. The interest-bearing base grows with every capitalisation, which is why the growth curve bends upwards rather than running in a straight line. The longer the horizon, the more of the final figure comes not from your contribution but from interest on interest already earned.
Use the calculator when you are planning a lump-sum investment with reinvested income: a term deposit with capitalisation, an accumulating fund or ETF, voluntary pension savings, or a corporate bond with reinvested coupons. If you are also making regular contributions on top of the starting amount, use the future value of regular contributions calculator. If the interest is paid out rather than reinvested, simple interest applies.
The formula explained in words
The final amount equals the principal multiplied by one plus the periodic rate, raised to the power of the number of periods: A = P · (1 + r/n)^(n·t). Accrued interest is the difference A − P.
- P — principal. The amount invested at the start of the period.
- r — nominal annual rate as a decimal: 5% means 0.05.
- n — capitalisations per year. 12 for monthly, 4 for quarterly, 2 for semi-annual, 1 for annual.
- t — term in years.
- r/n is the rate for a single period and n·t the total number of periods. At 5% with monthly capitalisation the monthly rate is 0.05/12 = 0.4167% and ten years contain 120 periods.
The key insight from the structure of the formula is that the term sits in the exponent while the rate sits in the base. One extra year at the start of a plan therefore counts for far more than one extra tenth of a percentage point of return. This is also where the rule of 72 comes from: money roughly doubles in 72 ÷ interest rate years. At 5% that suggests 14.4 years, while the exact calculation with monthly capitalisation gives 13.89 years.
A worked example
You invest €50,000 at 5% per year for 10 years with monthly capitalisation.
- Periodic rate: r/n = 0.05 ÷ 12 = 0.00416667.
- Number of periods: n·t = 12 × 10 = 120.
- Growth factor: (1 + 0.00416667)^120 = 1.647009.
- Final amount: A = 50,000 × 1.647009 = €82,350.47.
- Interest accrued: 82,350.47 − 50,000 = €32,350.47.
The same €50,000 at the same rate but with different capitalisation frequencies gives the following after 10 years:
| Capitalisation | Periods | Final amount | Interest accrued |
|---|---|---|---|
| Annual (n = 1) | 10 | €81,444.73 | €31,444.73 |
| Quarterly (n = 4) | 40 | €82,180.97 | €32,180.97 |
| Monthly (n = 12) | 120 | €82,350.47 | €32,350.47 |
| None (simple interest) | — | €75,000.00 | €25,000.00 |
Two conclusions are worth drawing. First, moving from simple to compound interest adds more than €7,300 on otherwise identical terms — that is the value of reinvesting. Second, the benefit of more frequent capitalisation is real but modest: going from annual to monthly earns roughly €906, under 2% of the interest accrued. Capitalisation frequency never makes up for a lower rate.
Practical guidance and the Bulgarian context
When comparing offers with different capitalisation frequencies, do not compare nominal rates — convert them to effective annual rates. A deposit at 3.90% with monthly capitalisation yields an effective 3.97% and beats a deposit at 3.95% with annual capitalisation, even though the headline number looks lower.
For tax planning, where the return accumulates matters. Individual income in Bulgaria is generally taxed at a flat 10%, while capital gains on shares and units traded on a regulated market in the EU or EEA are exempt for individuals — a material advantage of exchange-traded accumulating funds over interest-bearing products. Interest on bank deposits is subject to a final withholding tax whose current rate should be checked against the Personal Income Taxes Act in force. Tax lowers the effective rate and therefore weakens compounding itself, because the amount withheld no longer participates in later periods.
The formula also works in reverse: if you know the sum you need after a given number of years, divide it by the growth factor to find what you must invest today. For a €100,000 target in 10 years at 5% with monthly capitalisation you need 100,000 ÷ 1.647009 = €60,716.63.
Limitations of the calculation
The calculator assumes a constant rate throughout. That is a reasonable assumption for a fixed-rate term deposit but a heavy simplification for equities or funds, whose annual returns fluctuate. For those, treat the result as a scenario rather than a forecast — move the rate two or three points either way to see the range of plausible outcomes.
Management and custody fees, dealing commissions and taxes are excluded. A 1% annual management fee against a 5% gross return absorbs roughly a fifth of the interest accrued over ten years, which makes it one of the most underrated factors in long-term investing.
The result is in nominal euros and ignores inflation. It also assumes no interim contributions or withdrawals: the money is presumed to sit untouched for the full term. For plans with regular contributions use the future value of regular contributions calculator, and for deposits and withdrawals on irregular dates use XIRR.
Frequently asked questions
How is compound interest calculated?
The final amount follows A = P · (1 + r/n)^(n·t), where P is the principal, r the annual rate as a decimal, n the number of capitalisations per year and t the term in years. On €50,000 at 5% with monthly capitalisation over 10 years the growth factor is 1.647009 and the final amount €82,350.47. Interest accrued is the difference from the principal.
How much does capitalisation frequency matter?
Less than most people expect. On €50,000 at 5% over 10 years, annual capitalisation gives €81,444.73 and monthly gives €82,350.47 — a difference of about €906, under 2% of the interest earned. The gap between a 4.5% and a 5% return over the same period is several times larger. Look at the rate first and the frequency second.
How long does money take to double with compound interest?
The rule of 72 gives a quick estimate: divide 72 by the interest rate. At 5% that suggests about 14.4 years, while the exact calculation with monthly capitalisation gives 13.89 years. The rule is accurate enough for rates between 4% and 12% and is useful for a rough mental check without a calculator.
Does the calculator account for fees and taxes?
No, the result is gross. For a realistic figure, subtract the management fee from the rate before entering it: a 5% gross return with a 1% annual fee means entering 4%. Tax treatment depends on the product — capital gains on shares traded on a regulated EU or EEA market are exempt for individuals, while deposit interest carries a final withholding tax whose rate you should verify.
When should I use a different calculator?
If you make regular monthly or annual contributions, use the future value of regular contributions calculator. If you deposit and withdraw on irregular dates, XIRR is the most accurate measure. If you want the annual growth rate between two known values, use CAGR. This calculator covers a single lump sum left untouched for the whole term.
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The calculators are for guidance only and do not constitute financial, tax or legal advice. Parameters reflect 2026 legislation and should be verified annually. For a specific case, book a consultation with our specialists.