Periodic Compound Interest Calculator
Solve for total amount, principal, rate, or number of periods using the formula A equals P times one plus r to the power of t.
| Periods (t) | Total amount (A) | Interest earned (I) | Growth from start |
|---|---|---|---|
| 1 | $10,500.00 | $500.00 | 5.00% |
| 3 | $11,576.25 | $1,576.25 | 15.76% |
| 5 | $12,762.82 | $2,762.82 | 27.63% |
| 10 | $16,288.95 | $6,288.95 | 62.89% |
| 20 | $26,532.98 | $16,532.98 | 165.33% |
Periodic compound interest explained simply
Periodic compound interest explained simply means earning interest not only on the original amount of money but also on the interest that builds up from one period to the next. Each period the balance grows, and the next period’s interest is calculated on that larger, updated balance. This is what makes compound interest grow faster over time compared to simple interest, which only ever applies to the original principal.
The periodic compound interest formula
The periodic compound interest formula connects four variables, the accrued total, the principal, the periodic rate, and the number of periods, into a single equation.
In this formula, A is the accrued amount after compounding, P is the original principal, r is the interest rate per period written as a decimal, and t is the number of periods. The rate R is entered as a percent and converted internally using r equals R divided by 100. Periods can represent days, months, quarters, or years, as long as the rate and the number of periods use the same time unit consistently.
Solving for each variable
Solving for each variable in the compound interest formula follows directly from rearranging the original equation algebraically.
- Solve for total amount: A = P(1 + r)^t
- Solve for principal: P = A ÷ (1 + r)^t
- Solve for rate: r = (A ÷ P)^(1/t) − 1
- Solve for periods: t = ln(A ÷ P) ÷ ln(1 + r)
Worked example of periodic compound interest
A worked example of periodic compound interest shows how a starting balance grows over several periods. Suppose you deposit 10000 dollars at a periodic rate of 5 percent for 3 periods.
After 3 periods, the total accrued amount is 11576.25 dollars, which includes 1576.25 dollars of compound interest earned on top of the original principal.
How to use this compound interest calculator
How to use this compound interest calculator depends on which variable you are trying to find. Choose what you want to solve for from the dropdown, then fill in the remaining known values before selecting Calculate.
- Select the variable you want to solve for, such as total amount, principal, rate, or periods.
- Enter the known values into the remaining fields.
- Select Calculate to view the result and the full working steps.
- Select Clear to reset all fields and start a new calculation.
Periodic compounding versus compounding within a period
Periodic compounding versus compounding within a period is an important distinction in interest calculations. The basic formula on this page assumes compounding occurs exactly once per stated period. Some loans and investments compound more frequently within a single period, such as monthly compounding inside an annual rate, which requires a separate compounding frequency variable added to the formula.
Real world uses for compound interest
Real world uses for compound interest appear throughout savings accounts, loans, retirement planning, and investment growth projections. Banks use it to calculate how savings accounts grow over months or years, lenders use it to determine how loan balances increase, and investors use it to project long term portfolio growth.
- Projecting how a savings account balance grows over multiple years.
- Estimating retirement account growth based on periodic contributions and rates.
- Calculating how unpaid loan or credit balances increase over time.
- Comparing investment options with different periodic rates and time horizons.