# Accurate Compound Interest Calculator

This compound interest calculator calculates interest between any two dates. A dozen compounding periods are supported (did we miss any? :). You can also enter negative interest rates.

Because this calculator is date sensitive, and because it supports many compounding periods, it is a suitable tool for **calculating the compound interest owed on a debt**. You can use it to calculate accrued interest from a point in time when the balance is known. Because this calculator allows for odd days (example three months plus five days), you may calculate interest due for any investment or debt. *More details below the calculator*

### Information

## Compound Interest

Compound interest means that interest gets paid (or is earned) on previously unpaid interest.

To Quickly

Pick a Date

For example, if the interest rate is 2% and you start with $1,000 after the end of a year, you'll earn or owe $20 in interest (using annual compounding). Then at the end of two years, assuming there have been no withdrawals (or payments) you earn $20.40, not $20. The previous period's interest earned interest as well.

This pattern is called compounding, and it repeats as long as the money stays invested, or the debtor owes on the debt.

If you are an investor, you want to compound interest. If you are a debtor, you want to avoid it, particularly if you ever miss a payment or a payment is not enough to cover the interest due.

You can use this online interest calculator as a:

- apy calculator
- daily interest calculator
- investment interest calculator
- loan interest calculator
- negative interest rate calculator
- savings account interest calculator

As a side benefit to this calculator's date accuracy, you can use it for date math calculations. That is, given two dates, it will calculate the number of days between them, or it will find the date that is "X" days from the first date.

Enter an amount and a nominal annual interest rate.

Date Math: The number of days between the dates will get calculated when you change either date. If you enter a positive value for the number of days, the end date will be updated. If you enter a negative value for the number of days, the start date will be updated.

The above means you can calculate interest for a specific number of days and not worry about what the dates are. If you need to know the interest for 31 days, then enter 31 for the number of days and don't worry about the dates.

Set the compounding and days-in-year. Click "Calc." Interest and future value are calculated (FV is starting amount plus the interest.) Depositors should use the **Annual Percentage Yield ( APY)** calculation for comparing deposit accounts. It is the rate institutions must quote in the US for interest-bearing accounts. The Consumer Financial Protection Bureau defines APY in the Truth-in-Savings Act.

Interest may be calculated based on a unit of time, say a month. This is known as **"Periodic Interest"** In that case, a month's interest is always the same for the same interest rate and same principal balance regardless of the length of the month. Given $10,000 principal and an interest rate of 6.75% the interest will be the same for February as it is for March. Note if you select a periodic method such as "weekly", "biweekly" etc., and if the dates enter do not equate to a number of full periods, then interest will be calculated for the fractional period by counting the days and calculating simple interest. This generally results in 1/2 a month's interest being less than 1/2 of a full month's interest when using monthly compounding.

There is also **"exact day interest**." Interest is calculated based on the number of days. In this case, the amount of interest will be different for February and March. Set compounding to "continuous", "daily" or "simple" for daily interest calculations.

## Ivan says:

Please add “Monthly Deposit” amount instead of “Days in Year”. It will be perfect.

## Karl says:

There are already two calculators on the site that should do what you want.

Please see this savings calculator or try this future value of annuity calculator.

They both calculate compound interest and allow for monthly (or other deposit) frequencies. The latter calculator also creates a printable schedule which show periodic interest earned.

## Sergey says:

I found an error when I calculate interest earned for a month compounding annually. In this case the calculator shows APY as 12,68% which is obviously incorrect since with annual compounding it should be 12%

## Karl says:

You didn’t mention what annual interest rate you used. But, APY is a yield, not an interest rate. The equation used, is provided by the US Gov’t in the Truth-in-Saving Act and not something I just came up with. The calculator has proven to be correct for all test cases when compared with the examples in the regulation.

## Sergey says:

Thanks, Karl.

The annual interest rate I used was 12% compounding annualy. I rely only on simple math and not on any “Acts”. APY of 12,68% is a en error since there is no compounding during one year.

## Karl says:

I see. Than all I can say Sergey, is the calculation may not be what you want, need or expect, but it is not wrong.

Here’s the Truth-in-Savings Act equation for APY

US Law requires all depository institutions to provide depositors with the APY calculated as specified. This allows US consumers to compare results offered by banks and other depository institutions.

In your case, the reason why the yield is greater than 12% is because you are telling the calculator that the funds are deposited for only 30 or 31 days and you want your interest. You can then take the principal and interest and reinvest it (in effect compounding your return) and that’s why the YIELD is greater than the 12% interest RATE.

If you redo the calculation for 365 days, and used a 12% rate with annual compounding then the APY will be 12%.

## Micheal says:

Hi,

I need your help.

I changed the currency and date format but I could not find “save changes” button.

Can you please help me educate on this?

Thank you Sir.

Sincere Regards

Micheal

## Karl says:

Hello, my guess is, you are using a mobile device, right? If so, the change currency window might be too large. When you open the currency change window, try holding the device vertically so that you can see the bottom of that window. Let me know if that works, please.

I’ll work on making a better layout.

## Micheal says:

Hello Karl,

I am using W10 PC. I think I had not scroll further down whereby as I was not able to view because of the size of window.

It is perfectly fine now and I am able to save and set the currency and date format as I want.

Thank you for your help.

Sincere Regards

Micheal

## Karl says:

Thanks Micheal for letting me know.

## Emily says:

If we’re trying to calculate compound interest for a partial year what should the formula be? For example, if we assume we invested $100 at a 7% rate compounded annually for 100 days, should the formula be Interest = 100*(1.07)*100/365? Or should it be Interest = 100*(1.07)^100/365? The calculator seems to be using the former which provides an Annual Percentage Yield of greater than 7%.

Thanks in advance!

## Karl says:

Hi Emily, there are two types of questions I’m able to answer on this site. What calculator should I use to accomplish "X." And how do I use a calculator’s feature? I don’t have the equations in my head and if I started to research them again, I would spend more time doing that than building the site.

## Andy says:

Hello,

I am trying to calculate the return on a crypto currency that pays 6% every 5 days.

Any way I can use this calculator?

Thank you

## Karl says:

No, not with this calculator, or any of the calculators on this site. Sorry.

## Andy richardson says:

Thank you very much for your reply.

If you were me, how would you go about finding or making a calculator to display a 5-day ROI?

Thanks again,

Andy

## Karl says:

Use Google? Or perhaps Bing, or Duck Duck GO?

## Ajay Gupta says:

Hello Sir, i was trying to calculate compound interest for years that are in decimal. For example, if we assume we invested $100 at a 26% rate compounded annually for 1195 days and i use this basic excel formula =100*(1+26/100)^(1195/365) and result is 213.1132 and if i do the same calculations in your calculator it shows 214.14, please help to explain the difference.

Thanks in advance 🙂

## Karl says:

Hi, I don’t get involved in the details of the calculations. If I were to do that, I would not have time to work on the website. 🙂

However, if you want annual compounding, you have an error in your equation. The 1195/365 treats every day as the same. But for annual compounding, you have 3 years and 100 odd days (or 3 years and 99 odd days depending on the dates).

Use the calculator with these inputs, and you’ll see what I mean. They both are for 1,195 days, but they give different results, due to one date range includes leap year.

March 23, 2020

July 1, 2023

Result: 214.29 (no leap day)

and

March 24, 2021

July 1, 2024

Result: 214.14 (with a leap day)

Keep all other details the same, including the annual compounding.

## John says:

Good Evening Karl,

I have been using your calculator for several years and found it extremely helpful. However, I was using it today and it is returning different results with the exact same inputs. This happened on several occasions as I was very confused and wanted to make sure I didn’t enter anything incorrectly. I even went so far as to print a screen shot of the inputs to compare another attempt. Is there an issue with the calculator that is needing to be resolved? I would love to keep using this helpful tool, but need to be able to trust the results are accurate.

Thank you

## Karl says:

Hi John, I am not aware of any issues or bugs. Further, this particular calculator hasn’t had any changes, other than style changes, in years.

Nevertheless, I do take this seriously. Can you send me your screenshots? You can email them to the email address on the contact page, which I link to at the bottom of every web page.

## Karl says:

I just thought of something. When you say the exact same inputs, do you mean same dates too? Or are you thinking that if the number of days is equal, then the interest has to be equal if other facts are the same? Depending on details such as how compounding is handled, that is not always the case.

Or, was either date on the 28th, 29th, 30th or 31st?

## Karl says:

Hi John, I’ve been trying to get the compound interest calculator to give me different results with the same inputs, and I can’t. If you can provide details (a specific example), I know I can fix it.

To give you an example of what I mean by how two calculations that appear to be the same can have different results, take a look at the below. All details are the same, i.e 47 days, interest rate, amount etc. The difference is the dates. Because I selected monthly compounding the results are different because the number of odd days is different from May 15 to June 1 vs June 15 to July 1.

One other thing. Users will not see scenarios like this when they select exact, daily, or continuous compounding.

## John says:

Good afternoon,

The dates and other inputs were all the same. The issues only seemed to pop up if I was using the calculator for multiple calculations in the same sitting. It seems to work fine as long as the page is refreshed in between calculations. Unfortunately, because the issues are not consistent, I cannot recreate the issue easily and did not take a screenshot when they happened previously. It is almost like reuse causes an issue by carrying something forward when things are reset. It doesn’t make much sense based on its usual accuracy. I am sorry I could not provide more detail.

## Ken says:

How is it possible for compounding daily to result in a lesser apy than compounding weekly?

## Karl says:

Note that the interest amount is larger when you select weekly compounding – at least for the sample calculations that I checked.

It comes down to how many weeks are in a year. The calculator assumes 52 weeks per year, but that’s not really correct. There are 52.1428571428571 weeks in a year (364 / 7) but then that would not be correct for leap years.

When I do the math, assuming 10,000 invested for one week using weekly compounding, assuming 52.1429 weeks per year results in an interest amount that is 0.01 less than daily compounding for 7 days (for a 365 day year which is what the APY requires) and thus the APY is less.

I’ll consider changing the calculators to use a more precise number of weeks, but such a change will ( 1 ) impact all calculators and ( 2 ) take a while to implement if I do it.

On the other hand, this shows that the APY is doing what it is meant to do. It alerted you that weekly compounding is the more desirable choice when the institution paying interest assumes 52 weeks per year – there is no law in any state that dictates a standard that I am aware of.

## Karl says:

Note if I looks at Appendix J in Regulation Z see: 5(iv) (which is for APR not APY, but I don’t see the APY reg right now), it states:

Thus bi-weekly would be 26 weeks per year.