Dave's Math Tables: Interest and Exponential Growth

The Compound Interest Equation

A = P (1 + r/n) nt
    A = Total Amount (current worth)
    P = initial deposit or Principal
    r = annual interest rate (expressed as a fraction: eg. 0.06)
    n = # of times per year interest is compounded
    t = number of years invested

Simplified Compound Interest Equation

When interest is only compounded once per year (n=1), the equation simplifies to:
A = P (1 + r) t

Interest Compounded Continuously

When interest is compounded continuously (i.e. n --> ), the compound interest equation takes the form:
A = P e rt

Demonstration of Various Compounding

The following table shows the final amount (A), after t = 1 year, of an account initally with P = $10000, at 6% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect except on large balances or if compounding for many years.
1 (yearly)$ 10600.00
2 (semi-anually)$ 10609.00
4 (quarterly)$ 10613.64
12 (monthly)$ 10616.78
52 (weekly)$ 10618.00
365 (daily)$ 10618.31
continuously$ 10618.37