Daily Compound Interest Calculator

What this calculator does

Of all the ways interest gets added, daily compounding is the one you are most likely to actually meet. A lot of savings accounts use it, and so do credit cards. Each day, interest is worked out on your current balance and folded back in, so the next day you earn interest on a slightly bigger number, and it quietly builds from there.

This calculator shows you where that daily building lands. Put in a starting amount, a rate, and a number of days, and it tells you the future value and exactly how much of it is interest.

How to use it

Enter your initial value, the amount you are starting with. Then the interest rate, and here you get a small but useful choice: you can enter the rate as a daily rate or an annual one, using the dropdown beside it. Most accounts quote an annual rate, so that is usually the option you want, and the tool spreads it across the days for you. Finally, enter the time in days.

Working in days makes it easy to answer real questions, like how much a balance earns over a 90 day stretch, or across a full year of 365 days.

What you get back

Two figures. The future value, which is what your balance grows to over the days you entered, and the total interest, which is the part of that the compounding earned you. Simple to read, and the two together tell the whole story.

How daily compounding adds up

If you pick an annual rate, the tool first slices it into a daily piece by dividing by 365, then compounds that piece once for each day:

A = P × (1 + rate / 365)days

P is your starting amount, and the little exponent is the number of days. Each day multiplies your balance by a hair more than one, and those hairs stack on top of each other, which is what makes it compounding rather than plain interest. If you enter a rate that is already a daily rate, the tool skips the dividing step and simply applies it day by day.

A worked example

Say you put 10,000 into an account paying 5 percent a year, compounded daily, and leave it for a full 365 days.

The tool grows it to about 10,512.67, so you earn roughly 512.67 in interest over the year. Shorten it to a 90 day stretch and the same balance earns about 124. Notice that the yearly interest, 512.67 on a 5 percent account, is a touch more than the flat 500 you might have expected. That extra 12.67 is compounding at work, and the next section is about the number that captures it.

The number that really matters: APY

When you compare savings accounts, the stated interest rate is not the number to trust. The one to trust is the APY, the annual percentage yield, because it folds in the effect of compounding and tells you what you will truly earn in a year.

In our example, a 5 percent rate compounded daily works out to an APY of about 5.13 percent. That is why two accounts advertising the same rate can pay differently: the one that compounds daily earns a higher APY than one that compounds monthly. This matters enough that there is a law about it. Under the Truth in Savings Act, banks and credit unions in the US must show you the APY, precisely so you can compare accounts fairly without doing the compounding math yourself. When you shop, compare APY to APY.

Daily versus continuous

You may have seen the idea of continuous compounding, where interest is imagined to add at every instant rather than once a day. It sounds like it should earn a lot more. It does not. On our 10,000 at 5 percent for a year, the continuous version earns about four extra cents over the daily one. Four cents.

Daily compounding is so frequent that it sits right up against that theoretical ceiling. So if you ever meet an account boasting about exotic compounding, know that once you are compounding daily, a higher rate is worth chasing and fancier compounding is not. If you are curious about that theoretical ceiling, the Continuous Compound Interest Calculator shows it.

Questions people ask

Should I enter a daily or annual rate?

Whichever your account quotes. Most quote an annual rate, so pick "annually" and the tool divides it across the days. If you happen to have a true daily rate, pick "daily" and it applies it directly.

What is the difference between the interest rate and APY?

The interest rate is the plain stated rate. The APY includes the effect of compounding, so it reflects what you actually earn in a year. Daily compounding gives a higher APY than the same rate compounded monthly or yearly.

Do credit cards use daily compounding too?

Yes, many do, which is why a card balance can grow faster than a plain rate suggests. The same daily math that helps your savings works against you on a balance you carry.

Is daily compounding much better than monthly?

A little better, not dramatically. It shows up as a slightly higher APY. The bigger lever, by far, is the interest rate itself, so compare on APY and favour the higher one.

References

The compounding formula is standard. The rules on how yield must be disclosed come from federal law.

1. Truth in Savings Act, Regulation DD, 12 CFR Part 1030 (definition and disclosure of the annual percentage yield). https://www.ecfr.gov/current/title-12/part-1030
2. U.S. Securities and Exchange Commission, Investor.gov. Compound interest calculator and guidance. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator