# Compound Interest Calculator

This compound interest calculator calculates interest between any two dates. A dozen compounding frequencies 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 options, 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*

#### Info...

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## Compound Interest

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

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 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.

## Compound Interest Calculator Help

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.

## Mike says:

Did you make any recent changes to the site, i am no longer able to select, double click and copy any of the calculated information under “Days In Year”. This is a minor issue but i used this site a lot numerous times a day and being able to double click and copy that information saved me valuable seconds and minutes at my job, please advise.

## Karl says:

Yes, in fact some changes were released early Monday. But none of the changes should have impacted this calculator. (The changes were to the Mortgage Calculator and to the schedule and a new loan calculator widget was introduced.) That’s not to say that something didn’t go wrong. I’ll have to review.

But just to be clear, you’re saying that previously, you could click in the Days in Year input and it would be selected, and that would allow you to copy / paste the selection to another program. Do I get you? If so, I’m surprised it ever worked that way, that is, the item could be selected. Wait, I was just playing around, and I can select the text. This is what I did. I click just outside the box and dragged my mouse into the dropdown box while holding the mouse button down and the text was selected.

I’m wondering if, in the past, you may have just missed with the click and moved the mouse and the text got selected. Is that possible?

I really appreciate it when people take the time to comment on changes – particularly unexpected ones! That’s one of the challenges I have is trying to make changes in one place and not negatively impacting something else.

## Mike says:

Thanks for your response before previously I would be able to click on the calculated interest and the future total and selected copy and then paste it on another program just today I noticed that that function is no longer available and it is very useful for the type of work I do I haven’t tried clicking around and seeing if I can select it but when I tried to do it I get the circle with the line through it and it did not allow me to select copy and paste it elsewhere

## Karl says:

I’ll check, but I can select the results by clicking and dragging my mouse:

Interest Earned:

$1,002.74

Future Value (FV):

$11,002.74

Annual Percentage Yield (APY):

9.9986%

Daily Interest Rate:

0.0273%

## Mike says:

Karl,

I can also copy everything by clicking and dragging my mouse but up until yesterday I was able to click inside of “Interest Earned” and “Future Value” and select (either right click or Ctrl + V) only the calculated “dollar amount”. This option is no longer available. I’m sure this was just changed because I use the site probably 4 or 5 times per day.

## Karl says:

There has been no change to this calculator since about March. But I’m wondering if your browser has changed.

Using Chrome, it works as you say i.e. you can’t click to select the text in the result boxes.

But, when I use Internet Explorer v11, I can click (or double click) to select the text.

$1,002.74

$11,002.74

9.9986%

0.0273%

Even if you didn’t change browsers, it possible that an automatic update was applied on you computer to the browser and the browser’s behavior change with respect to readonly result fields.

## Venkata prasad says:

please tell me ms excel formula and general formula for calculation between two dates

## Karl says:

I never discuss formulas or equations. Generally a calculator does not use a single formula but rather several algorithms.

## Jitendra Patidar says:

Hi I am calculating the compound interest and finding different values what I am getting manually

Principal 200000 , Rate of interest 21 % , Duration 1 March 2014 to 29 Feb 2016

net amount manually is coming 292820

now principal 292820 , Rate of interest 36% , Duration 1 March 2016 to 3 Jan 2017

Net amount calculated manually is 379117

but in calculator the values are different . Kindly explain

I am using compound interest formula as P(1+r/100)^t

## Karl says:

Sorry, but as stated several times on this site, I don’t discuss the formulas. The support that I provide is limited to what calculator to use for a particular task and how to model a financial calculation.

One reason for not discussing the math or formulas is because there are just too many details. The formula you are using is incomplete. And you neglected to mention in your examples what compounding frequency you are using. If you don’t allow for the same compounding in the formula and while using the calculator, the results will be different.

## Mack says:

I believe I’ve found an error. I base this finding on other websites, my own calculation, and what a bank actually credited me.

(Numbers aren’t actual with bank, but example holds)

P = 2,000,000

R = 3.5%

Sept 1 – Dec 31 (121 days)

365 days in a year

Calculated Interest:

Annually compound: $23,205.48

Monthy: $23,161.54

How can monthly be less than annual?

I know you won’t discuss your formulas, but when I manually calculate annual using formal in google,

((2000000*(1+0.035/1)^(121/365*1))-2000000) =

Annual: $22,939.17

and then monthly $23,306.46

What gives?

(also, if I change the end date by 1 day to 1/1/17 on your calculator, the interest for monthly goes to $29,062.43. An increase of ~$5900 for 1 day. Are you doing some sort of payout schedule?)

I love the site and how you’ve implemented the calculator… but it has given me incorrect amounts.

Thanks!

## Karl says:

Thank you for your research and question. Are you ready for a long answer?

It has been said there are more ways than one to skin a cat (Seba Smith 1854), and there is certainly more than one way to calculate interest.

As you’ve discovered, we don’t use the same method. Whose right? I would say it’s up to the user to decide because neither method is necessarily wrong. Though I think I can make a very good case for why the method I use is the “correct” one. 🙂

The detail is in the concept of “compounding”.

Compound Interest:

You’ve selected “Annual Compounding” and use the compound interest formula. But, as you noted, the term is 121, which is not a year. Since the money has not been invested for even one compounding period, the compound interest formula should not be used. Rather the simple interest formula should be used i.e. P(rincipal) x (Rate / 365) x days.

As to the first monthly example, the term from Sept 1 to Dec. 31 is 2 months and some odd days. The calculation is thus more complex. There is both compounded interest and simple interest. When you add one more day, then the term is 3 full months. The simple interest goes away and you have the benefit of additional compounding. Thus the “larger” increase for just one more day.

Basically, with the technique you document, it prorates the effect of compounding. My approach does not.

What do you think?

## Mack says:

Thank you for the explanation. I had an guess that your calcs were doing something like you said, but I wouldn’t have expressed it as nicely as you.

As for who is ‘correct’… I agree that it’s up to the user. But for me, I was comparing to a bank’s calculations, and wasn’t able to calculate their ‘answer’ in any case. Hence the comment.

I’m not an accountant, but if the standard method is the ‘prorated’ method and not the (I’ll call it lump sum) lump sum method, then some sort of disclaimer might be warranted? I hate to ask you to start warning and disclaiming all cases. But, it does seem odd to have annual more than monthly.

Again, thank you much for your reply! It helps clarify greatly. I also greatly appreciate that you’re basically the only site that allows for days / partial periods in the calculations. (a couple sites do allow for decimal periods)

## Karl says:

Noted.

This has come up once before I think. I was thinking of adding an option that gave the user the choice between “prorated” compounding and “discreet” compounding. Then I got involved with other things and duly forgot about it. Thanks for reminding me. But perhaps giving users the choice might just add an unnecessary level of frustration?

I will say, that the method that is used here, is the method that is documented in U.S. Regulation “Z” – Truth-in-Lending Act.

And I’ll also add, that is why the APY is important. The APY will be the same for the same amount of interest on “X” principal for the same term regardless of the interest rate or the compounding selected.

Consumers should compare APY.

## Mack says:

Very excellent point about comparing APY!

## Karl says:

I don’t want to beat a dead horse here, but for the sake of others that may come along and read this, there are certainly cases where the interest would not be prorated for fractional compounding units (or odd days). Traditional US corporate bonds come to mind that pay semiannual compounded interest. If they are bought/sold between coupon dates, the accrued interest due the seller is simple interest – at least for the cases I’ve seen.

The bank you referenced uses “prorated” (my term) compound interest for the odd days, per your example. I wonder if this varies by location or jurisdiction? I don’t know. Perhaps a banker will chime in at some point.

## Skyhorse says:

Im trying to figure out what The total of $1875.00 with daily interest of 5% for the last 30 years would be

## Karl says:

Were you able to get the answer?

## Skyhorse says:

No i have not.

## PJ Johnson says:

If I am compounding interest daily and using a specific date range between interest rate changes, and it’s a leap year, how can I specify 366 days in the year?

## Karl says:

The calculator doesn’t support 366 day years.

I have thought about adding the feature and I don’t mind doing it. The math is certainly simple enough. However, I never understood what users would expect if the date range spanned 2 years, for example, Jan. 1, 2016 to Jan. 1, 2018. 2016 is a leap year. Would you calculate interest in 2 steps? What if the date range is April 1, 2016 – July 1, 2016, the 2nd quarter of a leap year. In that case would you still use 366 since the date range does not span February but it is within a leap year?

Of course, with this particular calculator, the user can make the decision. The difficulty arises with calculators that have a cash flow such as the Ultimate Investment Calculator where the user does not set days-per-year for each cash flow period.

I did run a calculation to see what the difference is between a 365 day year and a 366 day year. On one million dollars @ 5.0% for Jan 1, 2016 – Jan 1 2017, the difference is $144.00 $51,267.51 (366/366) v $51,411.51 (366/365).

I would be interested in knowing your thoughts.

## Adam Fleming says:

My utility company has been overcharging me, perhaps since 2009. I just found out they think we have a building with five apartments. It was an apartment building before we bought it, but we immediately converted it to single-family — and we told them so. We bought the house in October of 2008 but if we calculate from January of 2009 that would at least give me a ballpark figure. So, as far as we know, they overcharged us $44/mo ($11/service charge for each of 4 lines we don’t have) from January 2009 to September of 2016, (93 months they were charging us $55 instead of $11. We just thought it was normal!)

And in October 2016 when the price went up, and they began overcharging us at $14/line x 4, so that’s $56/mo too much, for the last 11 months, instead of $44. It’s a whopping 104 months of back pay!

The total without interest is around $4700 USD but what I’d like to know is what it would be with a modest 3% interest beginning with that first $44 back in January of 2009, and adding $44 to it each month, accruing interest… I can do it manually but it’s a lot of months, so there has to be a tool for this… plus I’m not sure if you really can get 3% a month, or if they would give us 3% APY, I know there’s a difference but not sure I can articulate what it is… I know it’s going to be hundreds of additional dollars. … Then, we will see if we can get them to cough it up… wish us luck…

## Karl says:

As you’ve discovered I assume, this calculator is for interest calculations on a single amount.

I’m not sure that I’ve been able to digest all the details, but you should be able to use the future value schedule to calculate the interest on a series of regular amounts over a number of years.

If the amounts are changing, then use the Ultimate Financial Calculator. Scroll down the page and see the tutorials. The one on future value would apply to your situation.

## Roy says:

Shouldn’t continuous compounded interest be the best paying at all times? I noticed that the interest earned goes up as the compounding frequency gets higher. That is until “every 4 weeks”, and then it seems to go down a little bit.

Example:

$5000, 1.25% interest, over 365 days, compounded daily: $62.89

$5000, 1.25% interest, over 365 days, compounded monthly: $63.06

$5000, 1.25% interest, over 365 days, compounded annually: $62.50

Why would monthly be the highest return?

## Karl says:

The dates are important. Using the default dates for how the calculator loads today, i.e. Aug. 16, the dates are Aug. 16, 2016 to Aug. 16. 2017 or 365 days.

I don’t get the results you are showing. I get, respectively:

$62.89

$62.86

$62.50

I’m wondering if something else was different when for your monthly calculation? If you don’t get what I indicated, please let me know your dates and I’ll recheck.

Did your 365 days span a leap year?

## Dinesh L says:

Hi Karl,

Your calculators are best and easy to calculate.

I met you in train today while coming back from Newark and I am really inspired meeting you and how passionately you are working on your hobby and writing code all the time to make your calculators best to use. Really Awesome!!

## Karl says:

Hi Dinesh, nice to meet you too. Hope to see you again. Thanks for stopping by the site! And of course, feel free to share it with your friends. :-).

## Terry says:

Can you help me I am trying to find out how to work out the following problem If I owe $511 in fees and I can be charged on top of fees already added into the total a further 9.5% per day- 93 days late How do I calculate this. There are other amounts with different days so actually need to know the process. Thank you for your help

## Karl says:

Do you actually mean 9.5% per day? If that’s the case, then you won’t be able to do that calculation with a single calculator on this site. All the calculators require the interest rate to be expressed as an annual number.

You can use this calculator and the third percentage calculator on this page.

Hope this helps.

## Mike says:

Why do you keep making changes. You had it perfect. SMH

## Karl says:

The only change I”m aware of on this page is the photograph and the addition of the search box. What’s not working for you? And on what device?

## julien says:

Hello –

Thanks for that tool.

Which formula do you exactly use for when you switch from 360 to 365 calculation for weekly or monthly calculation please ?

Any chance you have this calculator in excel to share ? that would be a lifetime saver!

Thanks,

julien

## Karl says:

You’re welcome. About the equations though, I never discuss them. On the other hand, I am available for consulting. You can reach me via the contact page

And no, this is not available in Excel.

## Christine says:

I have searched for days trying to find a calculator that will work out base amount + 2% daily interest, compounded monthly.

Microsoft Money will not download anymore on my newer computers. It was brilliant…..

## Evan Levine says:

I simply want to show the growth of 10,000 that earns varying interest each year – some years are positive and others negative. How can I do that?

## Karl says:

I’m not sure that I understand your question. So if my advice is not suitable, please ask again.

I think you should be able to use the ultimate financial calculator since it lets you change interest rates on any date.

You’ll probably want to set the schedule type to "Savings". If you try it, scroll down the page and see this tutorial:

There is also a tutorial about changing rates.