Exponential Growth and Compound Interest

Exponentials, logarithms and complex numbersComplex NumbersExponential Growth and Compound InterestLogarithms Binomial Theorem Rational Functions

Growth and decay

Growth or decay at rate r

y = a (1 \pm r)^{t}

Half-life

N (t) = N_{0} {(\frac{1}{2})}^{\frac{t}{t_{1 / 2}}} = N_{0} e^{- λ t}

λ = ln 2 / t₁/₂

Doubling time

N (t) = N_{0} \cdot 2^{\frac{t}{t_{d}}}

Compound interest

A = P {(1 + \frac{r}{n})}^{n t}

n compounding periods per year

Continuous compounding

A = P e^{r t}

Annual percentage yield

APY = {(1 + \frac{r}{n})}^{n} - 1

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