# Periodic Compound Interest Calculator

## Calculator Use

Using the compound interest formula, calculate principal plus interest or principal or rate or periods (time). Periods are any time units you want as long as you are consistent using the same base time units for periods and interest rate. Periods can be in days, months, quarters, years, etc.

## Compound Interest Equation

**A = P(1 + r) ^{t}**

Where:

- A = Accrued Amount (principal + interest)
- A = P + I
- P = Principal Amount
- I = Interest Amount
- R = Rate of Interest per period in percent
- r = Rate of Interest per period as a decimal
- r = R/100
- t = Number of Periods

Note that rate R, r and time t should be in the same time units such as months, quarters or years. R is entered in % but converted to r = R/100 and calculated in decimal form.

Compounding occurs once per period in this basic compounding equation but other calculators allow compounding more than once per period.

## Compound Interest Formulas and Calculations:

Compounding occurs once per period in this basic compounding equation but other calculators allow
compounding more than once per period utilizing
**A = P(1 + r/n) ^{nt}**.

- Calculate Accrued Amount (Principal + Interest)
**A = P(1 + r)**^{t}

- Calculate Principal Amount, solve for P
- P = A / (1 + r)
^{t}

- P = A / (1 + r)
- Calculate rate of interest in decimal, solve for r
- r = (A/P)
^{1/t}- 1

- r = (A/P)
- Calculate rate of interest in percent
- R = r * 100

- Calculate time, solve for t
- t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

**Example**: You want to know the annual return, or interest rate, you revieved on investment you made 2 1/2 years ago (30 months ago) of $50,000 that is now worth $58,400.

- Compounding occured annually
- Select "Calculate Rate (R)"
- Enter:

-- Total P+I (A): $58,400

-- Principal (P): $50,000

-- Number of Periods (t): 2.5

-- Answer: R = 6.4087% per period (year)

- Compounding occured monthly
- Select "Calculate Rate (R)"
- Enter:

-- Total P+I (A): $58,400

-- Principal (P): $50,000

-- Number of Periods (t): 30

-- Answer: R = 0.519% per period (month) - You can now use Nominal Interest Rate Calculator with period = month to find that an Effective Rate per Period of i = 0.519%, Compounded once per Period, m = 1, for Number of Periods n = 12, is 6.4088%/year.

## References

Weisstein, Eric W. "Compound Interest." From
*MathWorld*--A Wolfram Web Resource.
CompoundInterest.html

Principles of Accounting.com - Compound Interest

Compounding subtleties Margill.com - white-paper-interest.htm