Dave's Math Tables: Interest and Exponential Growth
(Math | General | Interest and Exponential Growth)

The Compound Interest Equation

P = C (1 + r/n) nt
where
    P = principal (current worth)
    C = initial deposit
    r = interest rate (expressed as a fraction: eg. 0.06)
    n = # of times per year interest in compounded
    t = number of years invested

Simplified Compound Interest Equation

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

Interest Compounded Continually

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

Demonstration of Various Compounding

The following table shows the final principal (P), after t = 1 year, of an account initally with C = $10000, at 6% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect.
nP
1 (yearly)$ 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

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