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CalcMax

Credit Card Interest Calculator

Range: 100 – 1,000,000

Range: 0 – 60

Range: 1 – 60

Range: 0 – 1,000,000

Range: 1 – 60

Result

72.74

Interest this cycle

Average daily balance
4,916.67
Daily periodic rate
0.04932%
Interest per day
2.4247
Interest if paid on the last day
73.97
Interest saved
1.23

A credit card does not charge interest once a month. It charges it every day, on whatever balance was outstanding that day, which is why two statements covering the same balance can ask for different amounts. The rate you are quoted is an annual percentage rate, but it is not divided by twelve: the card turns it into a daily periodic rate by dividing by 365, then applies that rate to each day's balance in turn. Money you pay stops accruing interest from the day it posts, so when inside the cycle a payment lands is worth real money — usually less than people hope, always more than nothing. This page assumes no grace period applies, because a grace period is a conditional thing rather than a permanent feature of a card: the conditions attached to it are disclosed when the account is opened, and in practice the condition is paying the previous statement in full. Once you are revolving, interest on a purchase generally runs from its transaction date rather than from the statement date. Enter the balance, the annual percentage rate, the length of the billing cycle, and the payment together with the day it posted, and this page returns the interest for that cycle, the average daily balance your statement prints, the daily periodic rate, the interest per day, and what the early payment saved against paying on the last day. On 5,000 at 18% over a 30 day cycle: leave it alone and the interest is 73.97. Pay 500 on day 25 and it falls to 72.74 — a saving of 1.23. Move the same 500 to day 1 and the interest is 66.82, which is 7.15 saved. Those numbers look small because a month is short. The same arithmetic on a balance you never clear is the reason it is still there. The cycle length moves the answer as much as the rate does: the identical 5,000 at 18% costs 73.97 over 30 days and 76.44 over 31, while the monthly shortcut of balance times rate over twelve would say 75.00 for both. Across a year of 31 day cycles that gap is worth more than the payment you moved.

5,000 at 18% over 30 days, paying 500 on different days

Payment dayAverage daily balanceInterest chargedInterest saved
14516.6766.827.15
54583.3367.816.16
15475070.273.7
254916.6772.741.23
30500073.970

One balance, one rate, one cycle, one payment — only the day it posts changes. The last column is the point: moving 500 to day 1 instead of day 30 saves 7.15, and moving it to day 15 saves 3.70. Both figures are small because a month is short and because the payment stops the clock only for the days that follow it. Read the middle two columns instead to see why: the average daily balance falls from 5,000 to 4,516.67 across the whole table, a drop of less than a tenth, while the payment is a tenth of the balance. That is the arithmetic behind the disappointment — paying early is worth doing, and it is never worth what the size of the payment suggests.

Formula

Daily periodic rate = annual percentage rate ÷ 365. Daily balance = the balance outstanding that day. Average daily balance = the sum of the daily balances ÷ the number of days in the billing cycle. Interest for the cycle = the sum of the daily balances × daily periodic rate, which is the same as average daily balance × daily periodic rate × days in the cycle.

B
Balance owed at the start of the billing cycle
P
Payment made inside the cycle, credited at the end of the day it posts
k
The day of the cycle on which the payment posts
N
Number of days in the billing cycle
d
Daily periodic rate: the annual percentage rate divided by 365
ADB
Average daily balance: the figure printed on your statement
I
Interest charged for the cycle

Use it when a statement's interest line does not match what you expected, because the mismatch is nearly always one of three things and this page isolates all three. First, the cycle length: a 31 day cycle costs more than a 30 day one at the same rate, and a statement that covers a long weekend can quietly be a 33 day cycle. Second, the day a payment posted: paying 500 on day 1 instead of day 25 saves 5.92 on the example above, and paying it a day before the cycle closes saves nothing at all. Third, the average daily balance itself, which is the one figure on the statement you can check this page against — if the two do not agree, the difference is new spending inside the cycle, and this page deliberately does not model that. What it also does not do is tell you what your card will charge next month: the balance here is frozen, and a card you are still using is not. Paying in full inside the cycle is worth seeing once, because it shows how little interest is left once the balance goes to zero early: on the same 5,000, clearing it on day 1 leaves 2.47 of interest instead of 73.97.

Worked examples

  1. 5,000 at 18% over 30 days, paying 500 on day 25

    1. Daily periodic rate: 18 ÷ 365 = 0.04932% a day, or 0.0004932 as a decimal
    2. Days 1 to 25 the balance is 5,000, so those 25 days contribute 125,000 of daily balance
    3. The payment posts at the end of day 25, so days 26 to 30 run at 4,500, contributing 22,500
    4. Sum of the daily balances: 125,000 + 22,500 = 147,500
    5. Average daily balance: 147,500 ÷ 30 = 4,916.67, which is the figure on the statement
    6. Interest: 147,500 × 0.0004932 = 72.74
    7. Had the 500 landed on day 30 instead, the sum would have been 150,000 and the interest 73.97, so the early payment saved 1.23

    The default, and the shape of every other row: the payment does not reduce the interest for the days that came before it, only for the days after. Because it posted on day 25 of 30, it moved the balance for five days out of thirty — a sixth of the cycle — and a sixth of the balance is not what gets saved. That is the whole reason paying early feels disappointing: the interest is charged on the balance that was there, day by day, and yesterday cannot be paid off today.

  2. The same 5,000 over a 31 day cycle, paying nothing

    1. The balance never moves, so the average daily balance is 5,000 and the sum of the daily balances is 155,000
    2. Interest: 155,000 × 0.0004932 = 76.44
    3. The same balance over 30 days would have cost 73.97
    4. Interest per day is 2.4658, so one extra day of cycle adds exactly that

    One day of billing cycle, one day of interest — 2.47 on a 5,000 balance. This is what separates daily from monthly accrual, and it is the number nobody expects: the monthly shortcut of balance times rate over twelve gives 75.00 for both the 30 day and the 31 day cycle, so it is 1.03 too high on one and 1.44 too low on the other. Over a year of 31 day cycles that shortcut understates the interest by more than 17, which is a whole extra day of interest every month that a monthly model never charges.

  3. Clearing the whole 5,000 on day 1

    1. Day 1 runs at 5,000, contributing 5,000 of daily balance
    2. The payment posts at the end of day 1, so days 2 to 30 run at zero
    3. Sum of the daily balances: 5,000
    4. Average daily balance: 5,000 ÷ 30 = 166.67
    5. Interest: 5,000 × 0.0004932 = 2.47
    6. Against 73.97 for leaving it until the last day, that is 71.50 saved

    Not zero. Paying the entire balance on the first day of the cycle still costs 2.47, because day one happened before the money arrived and interest is charged on the balance that was actually there. It is a good illustration of a rule that surprises people: paying off a card mid-cycle does not make the cycle free, and the only way to owe no interest at all is to have owed none at the start — which is what paying the previous statement in full buys you. That is the grace period, and it is the reason the second example above has no way back to zero.

Limitations

This page models one balance, one rate, one cycle and one payment, and it holds the balance still. New spending inside the cycle is absent, and that is the largest omission: a card you are still using has purchases landing on different days, each one starting to accrue interest on its own transaction date, and the average daily balance on a real statement is built from all of them. If your statement's average daily balance does not match the figure here, new spending is the first thing to suspect. Cash advances are absent, and they behave differently — most cards start charging interest on a cash advance from the day it is taken, with no grace period at any point, and often at a higher rate than purchases. Fees are absent: annual fees, late payment charges and over-limit fees can all be added to the balance and then accrue interest themselves. The 365 day divisor is the regulatory convention, but it is not the only one in use: issuers may instead assume a 360 day year with 30 day months when they produce the repayment estimates required on a statement, so a figure published by your card may not match this page to the cent. The rate is treated as fixed, while most cards carry a variable rate tied to a market benchmark, and a rate change partway through a cycle is not something a single rate can express. The billing cycle length is yours to type because no single number is correct: it is set by your statement, not by a rule. And nothing here is in any currency — 5,000 and 500 mean whatever unit you had in mind, and a daily interest figure is only meaningful once you attach one.

Frequently asked questions

How is credit card interest calculated on a daily basis?
The annual percentage rate is divided by 365 to get a daily periodic rate — 18% becomes 0.04932% a day. That rate is applied to the balance outstanding on each day of the cycle, and the results are added up. Interest is therefore charged on the balance that was actually there, day by day, not on a single month-end figure.
What is the average daily balance?
The sum of the balance on every day of the billing cycle, divided by the number of days in the cycle. A 5,000 balance paid down by 500 on day 25 of 30 gives 147,500 of daily balance over 30 days, so the average daily balance is 4,916.67. It is printed on your statement, which makes it the one figure you can check this page against.
Does paying early reduce the interest?
Yes, but only for the days after the payment posts. Interest for the days before it has already been earned on the higher balance. On 5,000 at 18% over 30 days, paying 500 on day 25 saves 1.23 against paying on the last day; paying the same 500 on day 1 saves 7.15. The saving is real and it is smaller than most people expect.
Why does a 31 day cycle cost more than a 30 day cycle?
Because there is one more day of balance to charge interest on. At 18% a 5,000 balance costs 2.47 a day, so the extra day is 2.47 more: 76.44 instead of 73.97. A monthly calculation that divides the rate by twelve gives 75.00 for both, which is why a monthly estimate and a real statement drift apart.
Is there a grace period on a credit card?
There can be one, but it is conditional rather than automatic, and the conditions have to be disclosed when the account is opened. In practice the condition is that you paid the previous statement in full: a grace period is the window in which new purchases can be repaid without a finance charge, and it is lost when a balance is carried. That is why this page assumes there is none, and why clearing a balance on day 1 of a cycle still costs a couple of days of interest.
Why does my statement not match this calculator exactly?
New spending is the usual reason, since purchases inside the cycle start accruing interest on their own dates and this page holds the balance still. The other candidates are a variable rate that moved, a cash advance charged differently from a purchase, fees added to the balance, and the issuer using a 360 day year rather than 365 when it produces the repayment estimates required on a statement.

References

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