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Finance Calc Kit
Investments

Periodic Compound Interest Calculator

Calculate compound interest per period using the formula A = P(1+r)^t. Solve for accrued amount, principal, interest rate, or number of periods.

Calculation mode

Inputs

$
%

Accrued amount (A)

$13,382.26

Interest earned: $3,382.26

Principal

$10,000.00

Starting balance

Accrued amount

$13,382.26

Principal plus interest

Rate per period

6.0000%

Periodic interest rate

Number of periods

5.0000

Compounding intervals

Principal vs interest

Accrued amount$13,382.26
  • Principal$10,000.0074.7%
  • Interest earned$3,382.2625.3%

Periodic compound interest formula

A=P(1+r)tA = P(1 + r)^t

A is the accrued amount, P is principal, r is the rate per period as a decimal, and t is the number of compounding periods.

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Periodic compound interest: solve for amount, principal, rate, or periods

Periodic compound interest applies a fixed rate once per compounding interval. Each period, interest is calculated on the current balance and added to principal, so future interest builds on prior gains. This calculator uses the standard TVM formula and lets you solve for any one unknown variable.

For annual-rate inputs with monthly or quarterly compounding frequency, use the compound interest calculator. To convert a stated annual nominal rate into the per-period rate before compounding, try the periodic interest rate calculator.

The periodic compound interest formula

A=P(1+r)tA = P(1 + r)^t
  • A: accrued amount (principal plus interest)
  • P: starting principal
  • r: interest rate per period (as a decimal)
  • t: number of compounding periods

Worked example

A $10,000 deposit earns 6% per period for 5 periods:

A=$10,000×(1+0.06)5=$10,000×1.3382255776=$13,382.26A = \$10{,}000 \times (1 + 0.06)^5 = \$10{,}000 \times 1.3382255776 = \$13{,}382.26

Total interest earned is $3,382.26, which is 33.82% of the original principal over five compounding intervals.

Solving for each variable

  • Accrued amount (A): multiply principal by (1 + r) raised to the power of t.
  • Principal (P): divide the accrued amount by (1 + r)^t.
  • Rate (R): solve r = (A/P)^(1/t) - 1.
  • Periods (t): solve t = ln(A/P) / ln(1 + r).

Frequently asked questions

What does rate per period mean?
Rate per period is the interest rate applied at each compounding interval, not the annual rate. If you have an annual nominal rate, divide it by the number of periods per year first, or use the periodic interest rate calculator.
How is this different from the compound interest calculator?
This tool works directly with the per-period rate and number of periods. The compound interest calculator accepts an annual rate and a compounding frequency such as monthly or quarterly.
Can I solve backward for principal or rate?
Yes. Use the mode selector to solve for accrued amount, principal, rate per period, or number of periods. Enter the three known values and the calculator finds the fourth.
Why must accrued amount exceed principal when solving for rate or periods?
A positive interest rate requires the ending balance to be larger than the starting principal. If accrued amount is less than or equal to principal, the investment did not grow and a positive rate cannot be computed.
Does this include recurring deposits?
No. This calculator models a single lump-sum principal with periodic compounding. For monthly contributions, use the investment calculator or future value calculator.
Are results stored on a server?
No. All math runs in your browser. URL parameters let you share or bookmark a specific scenario.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.