This compound interest calculator shows how a principal balance grows when interest is reinvested and earns interest of its own — compounded daily, monthly, quarterly, or annually. Add an optional monthly deposit to model a savings plan, and see your final balance, total interest earned, and effective annual yield (APY).
Compounding frequency matters because the more often interest is credited, the sooner it starts earning interest itself. Banks quote a nominal rate (APR), but the APY — which this calculator reports — is the true yearly growth rate after compounding.
The Compound Interest Formula
The standard compound interest formula is:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year (365 daily, 12 monthly, 4 quarterly, 1 annually), and t is time in years.
The effective annual yield converts any frequency to a comparable yearly rate:
APY = (1 + r/n)^n − 1
For example, 5% compounded monthly gives (1 + 0.05/12)^12 − 1 = 5.116% APY, and compounded daily gives 5.127%. The gap between frequencies is real but modest — the rate itself and the time invested matter far more.
Why Time Beats Frequency
Small differences compound into large ones over long periods:
- $10,000 at 5% for 10 years: $16,289 (annual), $16,470 (monthly), $16,487 (daily) — the daily-vs-annual gap is only $198.
- The same $10,000 left for 30 years at 5% monthly grows to $44,677 — time quadrupled the interest gap between any two frequencies.
- The Rule of 72 estimates doubling time: 72 ÷ rate. At 5%, money doubles in about 14.4 years; at 8%, about 9 years.
- Regular deposits amplify everything: adding just $100 per month roughly doubles the 10-year outcome in the example above.
Start early, contribute consistently, and let frequency be a tiebreaker rather than a deciding factor.
Example: $10,000 at 5% for 10 Years, Monthly Compounding
Deposit $10,000 at 5% APY compounded monthly, adding $100 at the end of each month, for 10 years.
The principal alone grows to $10,000 × (1 + 0.05/12)^120 = $16,470. The 120 deposits of $100 (totaling $12,000) grow to about $15,528.
Final balance: roughly $31,998. Total deposits were $22,000, so about $9,998 is interest. The effective annual yield is (1 + 0.05/12)^12 − 1 = 5.116%, slightly better than the 5.000% nominal rate.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the original principal and all previously earned interest. Unlike simple interest, which is paid only on principal, compounding makes the balance grow exponentially — each interest payment increases the base for the next one.
Is daily compounding better than monthly?
Slightly, but the difference is small. At 5%, daily compounding yields 5.127% APY versus 5.116% for monthly — about $11 more per year on $10,000. When comparing accounts, look at the stated APY, which already accounts for compounding frequency.
What is the difference between APR and APY?
APR is the nominal annual rate before compounding; APY is the actual yearly growth after compounding. APY = (1 + APR/n)^n − 1, where n is compounding periods per year. A 5% APR compounded daily equals a 5.127% APY, so APY is always the fairer comparison number.
How long does it take money to double with compound interest?
Use the Rule of 72: divide 72 by the annual rate. At 6%, money doubles in about 12 years; at 9%, about 8 years. The rule is an approximation of the exact formula t = ln(2)/ln(1 + r), and it is accurate within a few months for rates between 4% and 12%.
Does compound interest work against me on debt?
Yes. Credit cards typically compound interest daily on the outstanding balance, which is why a 24% APR is effectively about 27.1% APY. Paying only the minimum lets interest compound on interest, the same exponential force that builds savings — working in reverse.