Interest Calculator
Find the interest accrued on a balance over a number of days or months, with the amount that accrues per day and per month. Or project growth over years with monthly contributions and compounding from annual to daily.
One day of interest is principal × rate ÷ 365. A month counts as 1/12 of a year.
Added at the end of each full month.
How to use the Interest Calculator
- For accrued interest, enter the principal, the annual rate and the period in days, in months or as two dates. Then press Calculate Accrued Interest.
- Read off the interest accrued so far, the amount per day and per month, and the day-count basis the figures use.
- For growth over years with compounding and monthly deposits, switch to Growth over years, enter your numbers and press Calculate Growth.
The interest formulas
Compound: A = P (1 + r/n)^(n·t) · · · Simple: I = P · r · t
P is the starting balance, r is the annual rate as a decimal, t is time in years and n is the number of compounding periods per year. Growth over years compounds, so it pays interest on the principal plus the interest already added. Simple interest is paid on the principal only. The accrued interest calculator uses it, with t as the days in the period divided by 365 or 360. A monthly contribution goes in at the end of each full month and grows at (1 + r/n)^(n/12) − 1 per month for the rest of the term.
Worked example: 10 years of compounding
$5,000 at a 4.5% annual rate (APR) compounded monthly for 10 years gives A = 5,000 × (1 + 0.045/12)^120 ≈ $7,835. That rate works out to an APY of about 4.59%. At simple interest the same $5,000 would reach 5,000 + (5,000 × 0.045 × 10) = $7,250, so compounding adds $585. Add $100 a month and the balance comes to $22,954.77, made up of the $5,000 you started with, $12,000 in deposits, $2,835 of interest on the $5,000 and about $3,120 of interest on the deposits.
How to calculate accrued interest
Accrued interest is interest that has built up on a balance but has not been paid or credited yet. A loan accrues it between payments. A savings account accrues it between the dates the bank adds interest to the balance.
For simple daily accrual, accrued interest = principal × annual rate × days ÷ 365. Principal times rate is one year of interest. Dividing by 365 gives one day, and multiplying by the days in the period gives the total.
Dividing by 365 is the actual/365 day count, and the calculator uses it unless you pick actual/360. With a 360-day year each day accrues 365 ÷ 360 times as much, about 1.4% more interest at the same rate. Your loan agreement or account terms say which basis applies. On both, the calculator counts a month as one twelfth of a year.
Worked example: 90 days on $10,000 at 6%
Take an example balance of $10,000 at a 6% annual rate. One year of interest is 10,000 × 0.06 = $600. One day is 600 ÷ 365 = $1.6438, which the calculator rounds to $1.64. Over 90 days the accrued interest is 600 × 90 ÷ 365 = $147.95, and the balance with interest is $10,147.95.
One month, counted as a twelfth of a year, accrues 600 ÷ 12 = $50.00. Enter 10,000, 6 and 90 days under Accrued interest in the calculator above and it returns the same figures.
How compounding changes accrued interest
Simple accrual charges interest on the principal only, so every day adds the same amount. With daily compounding, each day's interest joins the balance and earns interest itself. Interest after d days is then principal × ((1 + rate ÷ 365)^d − 1).
In the example, daily compounding gives $149.03 after 90 days against $147.95 for simple accrual, about a dollar more. After a full year it is $618.31 against $600.00. The calculator shows the daily compounding figure beside the simple one, so you can see the gap for your own numbers.
What capitalized interest is
Capitalized interest is accrued interest that the lender adds to the principal instead of collecting it. From then on, interest accrues on the larger balance. If the $147.95 in the example were capitalized, the principal would become $10,147.95 and the daily accrual at 6% would rise from $1.64 to $1.67.
Your loan terms say whether and when interest capitalizes. To see what it costs, add the accrued interest to the principal in the calculator and run it again.
Other interest questions have their own pages:
- Simple interest calculator for non-compound interest over a term in years, months or days
- Compound interest calculator for savings growth when interest is reinvested
- Finance charge calculator for a credit card billing cycle or the full term of a loan
- Accrued interest day by day, with a loan example on a 365-day and a 360-day basis
How much does $10,000 earn at 4.5% APY?
$10,000 at 4.5% APY earns $450.00 in one year and $36.75 in the first month. Leave it untouched for five years and the interest adds up to $2,461.82, for a balance of $12,461.82.
The first month is not $450 ÷ 12 = $37.50. APY already counts compounding, so the monthly rate is 1.045^(1/12) − 1, about 0.3675%. Each month earns a little more than the one before because last month's interest is now part of the balance. The twelve months add up to exactly $450.00.
Every row in the table follows the same rule. One month is balance × ((1 + APY)^(1/12) − 1), one year is balance × APY, and n years is balance × ((1 + APY)^n − 1). The figures assume no deposits or withdrawals, a rate that stays fixed for the whole period, and interest before tax.
To check a row, switch the calculator above to Growth over years. Enter the balance, the APY as the rate, the number of years and Annually as the compounding frequency. $10,000 at 4.5% for 1 year then shows $450.00 of interest. On the default Monthly setting the calculator reads 4.5% as an APR compounded monthly and shows $459.40, because that APR works out to an APY of about 4.59%.
| Balance | APY | After 1 month | After 1 year | After 5 years |
|---|---|---|---|---|
| $1,000 | 4.0% | $3.27 | $40.00 | $216.65 |
| $1,000 | 4.5% | $3.67 | $45.00 | $246.18 |
| $1,000 | 5.0% | $4.07 | $50.00 | $276.28 |
| $5,000 | 4.0% | $16.37 | $200.00 | $1,083.26 |
| $5,000 | 4.5% | $18.37 | $225.00 | $1,230.91 |
| $5,000 | 5.0% | $20.37 | $250.00 | $1,381.41 |
| $10,000 | 4.0% | $32.74 | $400.00 | $2,166.53 |
| $10,000 | 4.5% | $36.75 | $450.00 | $2,461.82 |
| $10,000 | 5.0% | $40.74 | $500.00 | $2,762.82 |
| $25,000 | 4.0% | $81.84 | $1,000.00 | $5,416.32 |
| $25,000 | 4.5% | $91.87 | $1,125.00 | $6,154.55 |
| $25,000 | 5.0% | $101.85 | $1,250.00 | $6,907.04 |
| $50,000 | 4.0% | $163.69 | $2,000.00 | $10,832.65 |
| $50,000 | 4.5% | $183.74 | $2,250.00 | $12,309.10 |
| $50,000 | 5.0% | $203.71 | $2,500.00 | $13,814.08 |
| $100,000 | 4.0% | $327.37 | $4,000.00 | $21,665.29 |
| $100,000 | 4.5% | $367.48 | $4,500.00 | $24,618.19 |
| $100,000 | 5.0% | $407.41 | $5,000.00 | $27,628.16 |
Amounts that are not in the table
At a fixed APY the interest grows in step with the balance, so you can scale any row. $20,000 at 4.5% APY earns twice the $10,000 figures, which is $73.50 in the first month, $900.00 in a year and $4,923.64 over five years.
For a term in months, such as a 6-month or 18-month deposit, the CD calculator takes the APY directly:
Frequently asked questions
How do I calculate accrued interest?
Multiply the principal by the annual rate and by the number of days, then divide by 365. For example, $10,000 at 6% for 90 days is 10,000 × 0.06 × 90 ÷ 365 = $147.95. If your lender uses a 360-day year, divide by 360 instead, which gives $150.00.
How much interest accrues per day?
One day of interest is the principal times the annual rate, divided by 365. An example balance of $10,000 at 6% accrues $1.64 a day, and $25,000 at 7% accrues $4.79 a day. The amount stays the same every day unless the balance changes or the interest compounds.
How much interest accrues per month?
For an average month, divide one year of interest by 12. An example balance of $10,000 at 6% accrues $50.00 a month that way. Counted by actual days on a 365-day basis, the same balance accrues $49.32 in a 30-day month and $50.96 in a 31-day month.
What is the difference between accrued and compounded interest?
Accrued interest has built up but has not been paid or added to the balance yet. Compounding happens when it is added, because from then on it earns interest too. Over 90 days on an example balance of $10,000 at 6%, simple accrual comes to $147.95 and daily compounding to $149.03.
What is the difference between APR and APY?
APR is the simple annual rate. APY (annual percentage yield) bakes in compounding frequency. For a 5% APR compounded monthly, the APY is about 5.12%. Both calculators on this page expect the APR. If your bank only quotes an APY, enter the APY under Growth over years and choose annual compounding, which gives the same balance.
How do regular contributions change the result?
Each monthly contribution is added at the end of its month and earns interest for the months that remain, at whatever compounding frequency you pick. Deposits made late in the term have little time to grow, so most of the interest comes from early money.
Can I enter part of a year?
Yes. Under Growth over years, enter 0.5 for six months or 2.5 for two and a half years. Monthly contributions count only full months, so 0.6 years includes 7 deposits. For a period in days or between two dates, use the Accrued interest calculator instead.
Should I use simple or compound interest?
Your account or loan terms say which one applies. If interest is added to the balance and then earns interest itself, it compounds, so use Growth over years with the compounding frequency from your terms. If interest builds on the principal only until it is paid, use Accrued interest.
How much is 4.5% APY on $100,000 per month?
$367.48 in the first month. Over a full year $100,000 at 4.5% APY earns $4,500.00, an average of $375 a month, because each month earns a little more than the last as interest is added to the balance. This assumes no deposits or withdrawals and a rate that stays at 4.5%.
How much interest does $50,000 earn at 4.5% APY?
$2,250.00 in one year and $183.74 in the first month. Left for five years with nothing added or taken out, it earns $12,309.10, for a balance of $62,309.10. These figures are before tax.