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Rich Man, Poor Man - about the power of compounding

When interest is compounded, interest is paid on previously earned interest. 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:

- loan interest calculator
- savings interest calculator
- daily interest calculator
- negative interest calculator
- investment 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: If you change either date, days between dates will be calculated. If you enter a positive number of days, the end date will be updated. If you enter a negative 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.) **Annual percentage yield** is used for comparing investments. It is the rate institutions must quote in the US for interest bearing accounts. The holder of such an account can use the *APY* to compare different accounts.

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.

Calendar Tip: When using the calendar, click on the month at the top to list the months, then, if needed, click on the year at the top to list years. Click to select a year, select a month and select a day. Naturally you can scroll through the months and days too. Or you can click on "Today" to quickly select the current date.

If you prefer not using a calendar, single click on a date or use the [Tab] key (or [Shift][Tab]) to select a date. Then, as mentioned, type 8 digits only - no need to type the date part separators. Also, because the date is selected, you do not need to clear the prior date before typing. If mm/dd/yyyy is selected for the date format, for March 15, 2016, type 03152016.

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The compound interest calculator has been, over the years, one of the more popular financial calculators on this site. We hope you find it useful.

Please tell me how you use this calculator. Are you using it personally or professionally? What feature is important to you? If it didn't meet your needs, why? Your feedback will help me make improvements. Complete sentences aren't necessary! :)

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.

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.

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

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%

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.

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.

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

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

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

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.

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!

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?

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)

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.

Very excellent point about comparing APY!

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.