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A = P(1 + r/n)^(nt)

Compound interest calculator

See what a principal grows to when interest is added to the balance, with annual, half-yearly, quarterly, monthly or daily compounding.

Short answer: compound interest is P(1 + r/n)^(n·t) − P. ₹1,00,000 at 10% for 5 years is ₹1,61,051 with yearly compounding and ₹1,64,531 with quarterly — different totals from the same headline rate, which is exactly what the effective annual rate row shows.

Why the frequency changes the answer

Every time interest is added to the balance, the next period earns on a larger principal. Four additions a year therefore beat one, even though the quoted annual rate is identical. The effective annual rate normalises that: 10% compounded quarterly is 10.38% a year, and daily compounding pushes it to 10.52%.

Worked example

₹5,00,000 at 8% for 3 years, compounded half-yearly: 5,00,000 × (1 + 0.04)^6 = ₹6,33,298, so the interest is ₹1,33,298. Compare the yearly option on the same page — the gap is the effect of adding interest twice a year.

Estimate, not a bank statement. Taxation, TDS, premature-withdrawal penalties and the bank's own day-count convention are outside this arithmetic.

Compound interest questions

What is the compound interest formula?

A = P(1 + r/n)^(n·t), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the years. Compound interest is A − P. The page also shows the effective annual rate, (1 + r/n)^n − 1, which is what you actually earn in a year.

Why is quarterly better than annual at the same rate?

Because interest is added to the balance four times a year instead of once, so later periods earn on it. 10% compounded quarterly behaves like 10.38% compounded annually. The effective annual rate row makes that difference explicit rather than hiding it in the total.

How is daily compounding handled?

The year is treated as 365 days. Banks sometimes use 360 or the actual/365 convention, which changes the last rupee or two, so the result is an estimate rather than a statement of what a specific bank will pay.

Can I see the year-by-year growth?

Yes — the result lists the closing balance and interest to date at the end of every year, with a final row when the period is not a whole number of years.

Related tools

Simple interest calculatorInterest that is never reinvested.CAGR calculatorThe annualised rate behind a total return.SIP calculatorMonthly contributions instead of one lump sum.