Accurate Interest Calculator
A Brief Introduction to the Interest Calculator
This calculator determines the interest amount owed between any two dates. In addition to simple interest, it supports multiple compounding periods—currently more than a dozen. It also allows negative interest rates.
Because this calculator uses date-based calculations, it is well suited for determining interest owed on a debt. You can calculate accrued interest from any date for which the balance is known. More details appear below the calculator…
Related: If you need to calculate interest for a series of payments, deposits, or withdrawals, use the Future Value of an Annuity Calculator.
The Calculator-Calculate Interest Between Any Two Dates
To set your preferred currency and date format, click the “$ : MM/DD/YYYY” link in the lower right corner of any calculator.
Information
What is compound interest?
Compound interest is interest calculated on both the original principal and on any previously accrued interest. If you are paying—or earning—compound interest, the interest from earlier periods also earns interest.
For example, if the annual interest rate is 2% and you start with $1,000, you will earn or owe $20 after one year (using annual compounding). After two years—assuming no withdrawals or additional payments—the interest earned in the second year will be $20.40, not $20. This is because the first year’s interest also earned interest.
This process is known as compounding. It continues as long as the funds remain invested, or as long as the borrower continues to owe the debt.
If you are an investor, compounding works in your favor. If you are a borrower, compounding works against you—especially if you miss a payment or your payment does not cover the full interest due.
What is simple interest?
Simple interest is calculated only on the original principal amount. With a loan, interest is not charged on any unpaid interest. If you are a borrower, paying simple interest is generally more favorable. According to Dictionary.com, simple interest is “interest payable only on the principal.” Interest is never calculated on previously accrued interest.
Using the example above, if the annual interest rate is 2% and you start with $1,000, you will earn or owe $20 in interest after one year. Then, after two years—assuming no withdrawals or additional payments—you earn another $20.00, not $20.40. In simple interest, the prior period’s interest does not earn interest.
Other details
What is Annual Percentage Yield (APY)?
APY is the standardized yield financial institutions must disclose in the United States for interest-bearing accounts. The Consumer Financial Protection Bureau defines APY under the Truth-in-Savings Act. Use the APY to compare deposit accounts effectively.
What is the “Days In Year” option?
In finance, this is referred to as the “day count convention.”
You can select 360, 365, or 366 days in a year. The “Days In Year” setting affects interest expense calculations when using simple interest, daily compounding, or when the time span includes a fractional (or stub) period.
What is a fractional period? It refers to the extra days between two dates that are not sufficient to complete a full compounding cycle. For example, if compounding is set to “Monthly” and the dates are March 15 to April 20, there are five leftover days. These days form a fractional period—in this case, a fractional month.
Fractional periods can cause unexpected results in compound interest calculations. In some cases, a less frequent compounding schedule may produce a higher interest amount than a more frequent one.
What is continuous compounding interest?
Continuous compounding occurs when interest is calculated and reinvested in an infinite number of periods. It represents the mathematical limit of compounding frequency.
What is the impact of negative interest rates?
When interest compounds at a negative rate, the investor effectively pays a fee for holding funds. As a result, the future value becomes less than the present value. To better understand this, try a sample calculation using a calculator that supports negative interest rates—such as this one.
You can use this interest calculator as any of the following:
- APY calculator
- Daily interest expense calculator
- Investment interest calculator
- Loan interest expense calculator
- Negative interest rate calculator
- Savings account interest calculator
Thanks to its accurate handling of dates, this calculator can also perform date math. For example, given two dates, it can calculate the number of days between them or determine a future (or past) date based on a specified number of days.
Interest Equations
Compound Interest Equation
Fig. 2 – Step-by-step solution of the Compound Interest equation.
Variables: P = 10,000; r = 5%; n = 12; t = 1.
Variable Definitions
- P
- Principal amount (initial investment)
- r
- Nominal annual interest rate (expressed as a decimal)
- n
- Compounding frequency (e.g., 1 = annually, 12 = monthly, 52 = weekly, 365 = daily)
- t
- Total time the interest is applied (in the same time units as r, usually years)
- A
- Future value (includes both principal and interest)
Calculation Steps
- First, divide the annual rate by the compounding frequency: 0.05 ÷ 12.
- Add 1 to the result from Step 1.
- Raise the value from Step 2 to the 12th power.
- Multiply the result from Step 3 by 10,000.
Step-by-step Solution – Fig. 2
- 0.05 ÷ 12 = approximately 0.0041666667
- 0.0041666667 + 1 = 1.0041666667
- 1.004166666712 = approximately 1.0511618979
- 1.0511618979 × 10,000 = approximately 10,511.618979
Final Answer
The final answer (A) is approximately 10,511.62.
Validate the calculator. One-year, monthly-compounded interest.
| Starting Amount (PV): | $10,000.00 |
| Annual Interest Rate: | 5.0000% |
| Days (–9,999 < # < 47,482): | <calculated> |
| Start Date (year > 1969): | August 20, 2024 |
| End Date (year < 2100): | August 20, 2025 |
| Compounding: | Monthly |
| Days In Year: | N/A |
| Future Value (FV): | $10,511.62 |
Notes:
- This example uses the same calculation shown in Fig. 2.
- You can either enter two dates exactly one year apart (the calculator will determine the number of days), or—
- Enter a specific number of days (e.g., 365 or 366 if the period includes February 29), and the end date will be calculated.
- The “Days In Year” setting has no effect in this example, because the period spans exactly twelve months with no extra days.
- With monthly compounding, the total interest for a full year will be the same whether the year has 365 or 366 days.
Simple Interest Equation
Fig. 4 – Step-by-step solution of the Simple Interest equation.
Variables: B = 10,000; r = 5%; n = 12; m = 12.
Variable Definitions
- B
- Initial balance
- r
- Simple annual interest rate (expressed as a decimal)
- n
- Frequency with which interest is applied
- m
- Number of time periods elapsed
- A
- Future value of the investment (principal plus interest)
Calculation Steps
- Multiply the principal amount ($10,000) by the rate (0.05) and the number of time periods (12).
- Divide the result from Step 1 by 12.
- Add the result from Step 2 to the initial balance.
Step-by-step Solution – Fig. 4
- 0.05 × 10,000 × 12 = 6,000
- 6,000 ÷ 12 = 500
- 500 + 10,000 = 10,500
Final Answer
The final accumulated amount is 10,500.
Validate the calculator. One-year simple interest.
| Starting Amount (PV): | $10,000.00 |
| Annual Interest Rate: | 5.0000% |
| Days (–9,999 < # < 47,482): | <calculated> |
| Start Date (year > 1969): | August 20, 2024 |
| End Date (year < 2100): | August 20, 2025 |
| Compounding: | Exact/Simple |
| Days In Year: | 365 |
| Future Value (FV): | $10,500.00 |
Notes:
- This is the same calculation shown in Fig. 4, except with m = 365 and n = 365.
- For simple interest, the calculator always uses days as the time unit. Therefore, 12 months and 365 days produce the same result: ((0.05 × 10,000 × 365) ÷ 365) + 10,000 = 10,500.00
- You can either enter two dates exactly one year apart (the calculator will determine the number of days), or—
- Enter a value for the number of days (e.g., 365 or 366 if February 29 is included), and the calculator will determine the end date.
- The “Days In Year” setting determines the value of n. The “Days” field corresponds to m.
- Because interest is calculated daily, and months have different lengths, the interest for each month may vary. This also applies in leap years.
Interest Calculator Help
Enter a principal amount and a nominal annual interest rate.
Date math: The calculator determines the number of days between the start and end dates automatically when either date is changed. If you enter a positive value for the number of days, the end date is adjusted. If you enter a negative value, the start date is adjusted.
This allows you to calculate interest based on a specific number of days without needing to set exact calendar dates. For example, if you want to calculate interest for 31 days, simply enter 31 in the “Days” field—no need to adjust the start or end date.
Choose the compounding method and the number of days in the year, then click “Calc.” The calculator will compute the interest and the future value (FV), which is the original amount plus interest. For depositors, use the Annual Percentage Yield (APY) calculation to compare accounts. In the United States, APY is the required disclosure rate for interest-bearing accounts. The Consumer Financial Protection Bureau defines APY in the Truth-in-Savings Act.
Interest may also be calculated based on fixed time intervals (e.g., one month). This is known as periodic interest. In this case, monthly interest remains the same for the same rate and balance, regardless of how many days are in the month. For example, with a $10,000 balance and a 6.75% interest rate, February and March will produce the same interest amount.
If you select a periodic method such as “weekly,” “biweekly,” etc., and the selected date range does not cover an exact number of full periods, the calculator will apply simple interest to the remaining (fractional) period. This often results in interest for a partial period being less than a proportional fraction of a full period. For example, half a month’s interest may be less than 50% of a full month’s interest when using monthly compounding.
The calculator also supports exact-day interest, where interest is based on the actual number of days in the period. In this mode, interest for February and March will differ. To use exact-day interest, set the compounding method to “continuous,” “daily,” or “simple.”
mike says:
can your compounding calculator show and print out the schedule for the dates that are imputed?
Karl says:
This future value of an annuity calculator will allow you to print out a compounded interest schedule with the dates.
Is that what you mean?
Mike says:
Why can’t I Ctrl-V paste a number into the starting amount section. I’ve been using this webpage for years and this is something that was recently changed. Any reason why???
Karl says:
I was not aware of this change. It was not intentional.
I updated the code about 3 months ago to stay current with changes and enhancements found in new browsers.
I will review how the my code handles user inputs to see if I can allow paste to work again, but it will be a while before I can get to it. My plate is pretty full.
On the other hand, hopefully you know when you tab to an input (or click in it) the value is selected. You do not need to clear it. You can simply start typing. So if you had to enter say 500,000, it might be just as fast to type the 6 digits than selecting a number from another location, copying it, and then pasting it into the calculator.
But as I say, I’ll look into this.
Curt says:
Hi, I am trying to calculate a payoff for a loan I made that is compounding monthly over 136 days with no payments. This appears to be correct calculator, but I cannot input the interest rate and hit Calc. Am I doing something wrong or do I have to have a paid subscription of some sort for doing only one calculation? Thank you.
Karl says:
No one ever needs a subscription to do a calculations. The number of calculations one can do for any calculator on this site is unlimited.
Did you happen to change the currency or date settings?
Can you give me the inputs you are trying? I see no reason why you can enter an interest rate. I just tried it and the calculator worked from my location.
Curt says:
Sorry, operator error 🙄
Karl says:
Good to hear it worked for you! Thanks for letting me know.
Mike says:
Hey Karl, I’m Mike from the above message on 01/17/24 with the Ctrl-V issue. I been working around this matter but just wanted to check to see if you had a chance to fix this issue. Thanks for your time, as always.
Karl says:
Hi Mike, you should be able to both copy and paste values now. If paste doesn’t work for you right away, you may need to do a hard refresh with your browser.
Mike says:
Nope. Pasting in the starting amount section via “Ctrl-V” still does not work.
Karl says:
I’m sorry that pasting is still not working for you.
I just pasted these two numbers into amount:
20,999.88
$30888.99
Using Ctrl-V on Windows with Chrome.
I first copied the number, then clicked in the amount input which left the value currently there selected. I typed Ctrl-V and the number that was there was replaced with the number I had copied.
Are you copying from a text file? If you are copying from a PDF or a Word file, there may be some hidden values or characters that break pasting.
Also, you can try doing a hard refresh of the web page to make sure that the latest version of the code is downloaded to your browser. If your browser didn’t get the update, then pasting would not work.
If nothing works for you, please give me the values you are trying to paste, and I’ll continue to look at this.
About hard refreshing the page:
Depending on your operating system, all you need to do is type the following key combination:
Above, from Refresh Your Cache
Linds says:
I am using the Accurate Interest Calculator and it ties to what I am calculating on my end for Simple loans, however, for annual compounding, I am unable to tie out.
I have a start date mid-month, and it appears to not be including a portion of the midmonth at the end of the year.
Karl says:
The mid-month (called the stub period) is the initial period, not the last period (at least from this calculator’s perspective and the U.S. Truth-in-Lending Act.)
Thus, with annual compounding if you enter Dec. 15, 2024 as the start date and Jan. 1, 2026 as the last date, the stub period is Dec. 15 to Jan. 1, 2025.
Carlos Castiglia says:
La calculadora de interés compuesto y simple no tiene la opción de poner el tiempo en meses, lo hace solo en días y es muy difícil y lleva mucho tiempo calcular el tiempo justo. Hay alguna alternativa para poder trabajar en meses? Gracias