Compound Interest Calculator

How to use this calculator

1. Enter the interest rate you have been quoted.
2. Choose the compounding period that rate is quoted on — monthly for most cards, daily for many savings accounts.
3. Choose the period you want it converted to. Annually gives you the APY.
4. Press Calculate to see the equivalent rate, and the ladder below it to see what the same rate earns at every period.

This converts rates. To work out what a balance actually becomes over time, use the interest calculator.

Why a rate means nothing on its own

A quoted rate is only half a fact. The other half is how often it compounds, because interest that is added sooner starts earning interest of its own. That is why 6% compounded monthly and 6.16778% compounded annually are the same deal: the first adds 0.5% twelve times, and each addition spends the rest of the year earning too.

Two lenders can quote you different numbers for identical debt, and two banks can quote different numbers for identical returns. Converting both to the same period is the only way to tell which is actually better.

APR and APY

APR is the nominal rate — the headline, before compounding is counted. APY is what a year actually costs or earns once it is. They are the same number only when interest compounds annually; every other period makes the APY higher.

The gap widens with the rate. At 6% compounded monthly the APY is 6.16778% — about a sixth of a point. On a credit card at 24.99% APR, the same monthly compounding makes the real annual cost 28.06%: over three points, and the part of the number nobody advertises.

The formula

Every rate reduces to one effective annual rate, and that shared ground is what lets any two periods convert:

APY = (1 + r / n)ⁿ − 1

• r — the nominal rate as a decimal (6% is 0.06)
• n — compounding periods per year (12 for monthly, 365 for daily)

Going the other way — from an effective rate back to a nominal one at some period — is the same formula rearranged: r = n × ((1 + APY)^1/n − 1). Continuous compounding is the limit as n grows without bound, where the pair becomes e^r − 1 and ln(1 + APY).

How much compounding frequency is actually worth

Less than most people expect, and with sharply diminishing returns. Here is 6% at every period:

Compounded	Effective annual rate	Gained over annual
Annually	6.00000%	—
Semi-annually	6.09000%	0.090
Quarterly	6.13636%	0.136
Monthly	6.16778%	0.168
Daily	6.18313%	0.183
Continuously	6.18365%	0.184

Monthly compounding captures about 91% of everything continuous compounding could ever give you. The whole distance from daily to the theoretical ceiling is five thousandths of a percentage point. A bank advertising daily compounding over monthly is advertising almost nothing; the rate itself is what matters.

The gap grows with the rate, though. At 20%, annual compounding earns 20% and monthly earns 21.93911% — nearly two full points. Compounding frequency matters most exactly where the rate already hurts.

Where you meet each period

• Daily — most savings accounts and credit-card balances.
• Monthly — mortgages, car loans, and the APR quoted on cards.
• Quarterly / semi-annually — some bonds and certificates of deposit.
• Annually — the APY banks must advertise, and how returns are usually compared.
• Continuously — a theoretical ceiling used in pricing models, not a product.

Limitations to keep in mind

• This converts a rate. It does not project a balance — use the interest calculator for that.
• It assumes the rate is fixed. A variable rate converts the same way, but only for as long as it holds.
• It ignores fees. A quoted APR that includes fees is not a pure compounding rate, and converting it will not isolate them.
• Tax is not modelled, and it can matter more than compounding frequency ever does.

To project what a balance grows to, use the interest calculator; to plan regular deposits, the savings calculator. This is general educational information, not financial advice.