How the balance is worked out on this page
A certificate of deposit pays interest on a fixed sum for a fixed term. The interest is added to the balance at regular intervals, and from then on the added interest earns interest as well. The end balance is what the deposit turns into by the end of the term, and the total interest is the end balance minus the deposit.
rate per period = annual rate / how many times a year the interest is added
number of periods = term in months × how many times a year / 12
end balance = deposit × (1 + rate per period) ^ number of periods
total interest = end balance minus deposit
The page prints every one of those steps with your own numbers under the result, rather than only the last figure, so you can follow it and check it. Here it is with an example, 10,000 in for 60 months at 4.5% a year, added to the balance twelve times a year:
Deposit = 10,000.00
Annual interest rate = 4.5% = 0.045 as a decimal
Rate per period = 0.045 / 12 = 0.00375
Term = 60 months
Periods = 60 months × 12 / 12 = 60
Growth over the term = 1.00375 ^ 60 = 1.25179582
End balance = 10,000.00 × 1.25179582 = 12,517.95
Total interest = 12,517.95 - 10,000.00 = 2,517.95
Effective annual rate (APY) = (1.00375 ^ 12 - 1) × 100 = 4.59%
So 10,000 becomes 12,517.95, which is 2,517.95 of interest. The effective annual rate is 4.59% and the rate on the certificate is 4.5%, and the two are different because the interest is added to the balance twelve times over the year, so part of the year's interest earns interest in the same year. The more often interest is added, the wider that gap gets.
Every figure is cut off downwards, never rounded up
One line, and it is the rule everywhere on this site: nothing here is ever rounded up. The annual rate as a decimal and the rate for each period are shown to twelve decimals, the growth over the term to eight, the money to the cent, and the effective annual rate to two, and each figure is cut off at that point rather than brought to the nearest. The figure on the screen is therefore never higher than the number it came from.
Each line of the working is worked out from the line above it exactly as that line is printed. Check the arithmetic with the figures on the screen and the last step lands on the printed answer, instead of a hundredth away from it. The money is carried in whole cents from the balance line to the interest line, so the subtraction you see is exactly the subtraction that was done.
A spreadsheet does not cut figures down the way this page does, so on the same four inputs the last cent can come out differently. The spreadsheet section below sets out both routes.
What the four boxes mean, and what is not counted
Initial deposit is the money you put in on day one, taken to the cent. It is the whole of the money the page looks at. Nothing is added to it during the term and nothing is taken out.
Annual interest rate is the rate published on the certificate, in percent a year. It is not the APY, and entering an APY here gives an end balance that is too high: the page works the APY out from this rate rather than the other way round. The rate is used exactly as typed, so 4.5 and 4.50 give the same figures and 0.045 would be read as a rate of less than one twentieth of one percent.
Term is how long the money is locked in for. Months are the unit the sum is done in. A term typed in years is multiplied by twelve before anything is worked out, and the number of periods comes from the months and from the compounding, so a term that does not divide evenly into periods is handled by working with a part period rather than by silently dropping it.
Interest added to the balance is how many times a year the interest is credited. It changes the answer: the same rate over the same term gives a higher end balance when the interest is added more often, because the credited interest starts earning interest sooner.
Taxes are not deducted, and neither is anything added back for them. A CD pays interest that is generally taxable as income, and this page has no box for a tax rate, so the end balance here is before any tax. Early withdrawal penalties are not counted either: the page assumes the money stays in for the whole term. Account fees, minimum deposit rules and any rate that changes during the term are outside it as well. Everything comes from the four boxes and nothing is fetched from anywhere.
What happens when the rate is below zero
A negative rate is accepted on this page, and it gives a balance below the deposit and a negative total interest. That is the arithmetic and not a mistake. The rate for each period is negative, so the figure that the balance is multiplied by is below 1, and multiplying by something below 1 shrinks the amount instead of growing it. Here is 10,000 for 12 months at minus 5% a year, added to the balance twelve times a year:
Rate per period = -0.05 / 12 = -0.004166666667
Growth over the term = 0.995833333333 ^ 12 = 0.95113006
End balance = 10,000.00 × 0.95113006 = 9,511.30
Total interest = 9,511.30 - 10,000.00 = -488.70
Effective annual rate (APY) = (0.995833333333 ^ 12 - 1) × 100 = -4.89%
Read that as 488.70 less than the money that went in, and as an effective annual rate of minus 4.89%. The minus sign in front of the interest is the fall, and the note under the result says in words that the end balance is below the deposit. The yearly figure is a little further below zero than the rate on the certificate, which is the same compounding effect working in the other direction: the balance is being multiplied by a figure below 1 several times over the year rather than once.
The growth over the term is what decides which way the balance moves. Above 1 the balance grows, at exactly 1 it stands still, and below 1 it shrinks. That single line is printed under the result whatever you enter, so you can read the direction off the working rather than off the sign of the rate alone.
What happens with an empty box, a zero, or a number out of range
These are the cases that decide whether a calculator can be checked, so this page gives each of them an answer that can be read, and says which one it is rather than going quiet.
- An empty box. Nothing is worked out and nothing is shown. The result area is emptied rather than left holding the last figures, so there is never a number on the screen that does not belong to what is typed in the boxes. The line under the button says which box is still needed.
- A deposit of 0. Worked out rather than refused. The end balance is 0.00 and the total interest is 0.00, because there is no money for the rate to be paid on, and the note under the result says exactly that. The rate and the term are still used, they are simply applied to nothing.
- A rate of 0. Worked out. The growth over the term is 1, the end balance equals the deposit, the total interest is 0.00 and the effective annual rate is 0.00%.
- A deposit below 0. Not worked out. A negative deposit is not a certificate of deposit, and the line under the button says so.
- A term of 0. Not worked out. With no time passing there is nothing for the interest to be paid over. Months are the unit here, so a term of 0 means 0 months whatever the unit is set to.
- A deposit above 1,000,000,000. Not worked out, and the line under the button gives the limit.
- A rate outside minus 100% to 100% a year. Not worked out. Below minus 100% the rate for each period stops describing anything, and above 100% a year the figure stops describing a CD.
- A term above 1,200 months. Not worked out. That is 100 years, and past it this page is the wrong tool.
- A balance above about a trillion. Not worked out. At that size the cents on the end stop meaning anything, so the page says it cannot give a figure instead of printing one that cannot be trusted.
The limits are listed here so that they are not a surprise: every one of them is a line under the button in words, not a blank result area.
What this page cannot work out
The four boxes are the whole input. These things are outside it, and none of them is a rounding difference:
- Tax. The page has no tax box, so the interest shown is before tax. Working out the after tax figure needs your own marginal rate, and that is not part of this sum.
- An early withdrawal penalty. The page assumes the money stays in for the whole term.
- A rate that changes during the term. This is a fixed rate CD and nothing else. A bump up CD, a step rate CD and a variable rate CD all need more than one rate, and there is no box for a second rate here.
- Money added or taken out during the term. The deposit is one figure on day one. A partial withdrawal is not a smaller deposit for the whole term, and nothing on this page can be used as if it were.
- Comparing two CDs. The page works out one CD at a time. To compare two, run it twice and compare the two printed workings.
- What happens next. The page works from four figures you typed, for a term that is already decided. It does not carry those figures forward to any other date, and nothing on it says anything about future rates.
There are no live rates anywhere on this page. The deposit, the rate, the term and the compounding are all typed by you and no quote is fetched, so every figure on the screen traces back to your own four entries.
The same sum in a spreadsheet
Both routes use the same four things. Put the deposit in A1, the annual rate in percent in A2, the term in months in A3 and how many times a year the interest is added in A4.
=A1*(1+A2/100/A4)^(A3*A4/12)
That is the end balance. The total interest is that cell minus A1:
=A1*(1+A2/100/A4)^(A3*A4/12)-A1
The effective annual rate, as a percent, is the same rate per period compounded A4 times over one year:
=((1+A2/100/A4)^A4-1)*100
On the example above that last line gives 4.59. With the deposit of 10,000 in A1, the rate of 4.5 in A2, the term of 60 in A3 and the compounding of 12 in A4, the first formula gives 12,517.95, which is the figure this page prints.
One difference is worth knowing about: a spreadsheet rounds a number when it displays it but keeps the full value underneath, while this page cuts every figure down at the point shown and works the next line from what it printed. On the same four entries a last cent can differ, and when it does, this page is the one that matches the working printed above it.
The same deposit, other questions
A CD answers one question about money sitting still for a fixed term. Two others come up beside it. If the money is in a share rather than a certificate and you want the rate it grew at, the CAGR calculator works that out from what the position cost and what it was worth, with the same printed working. If you want to know what happens when you add to a holding on a regular schedule instead of once, the DCA calculator works that out buy by buy. And if the money is in a dividend payer, the dividend calculator and the dividend reinvestment calculator take it from there.
Frequently asked questions
How is CD interest calculated?
Divide the annual rate by how many times a year the interest is added to the balance, which gives the rate for one period. Add 1 to it. Raise that to the number of periods in the term, which is the term in months times how many times a year divided by 12. Multiply the deposit by the result and you have the end balance. Subtract the deposit and you have the total interest. On the example above: 4.5% a year with monthly compounding is a rate of 0.00375 for each period, 1.00375 to the power of 60 is 1.25179582, and 10,000 times that is 12,517.95, which is 2,517.95 of interest.
What is the difference between the rate and the APY?
The rate on the certificate is the figure the bank publishes, and the APY is what that rate comes to over a year once the interest added during the year is itself earning interest. This page asks for the published rate and works the APY out, and both are shown: on 4.5% added twelve times a year the APY is 4.59%. The gap widens as the rate rises and as the interest is added more often, and it closes to nothing when the interest is added once a year, where the rate and the APY are the same figure. Entering an APY where the rate belongs gives an end balance that is too high, which is why the box is labelled for the rate and the hint under it says so.
Does it matter whether interest is added monthly or daily?
It matters, and this page shows you how much. On 10,000 for 12 months at 5% a year, adding the interest once a year gives 10,500.00, twelve times a year gives 10,511.61, and 365 times a year gives 10,512.67. The differences are small in money terms at these rates, and the daily figure is the highest of the three, because credited interest starts earning interest sooner. The page will not tell you which one a given bank uses: that is in the account terms, and the compounding box is there for you to set it to whatever the certificate actually says.