Compound Interest

• Interest earned at the end of a period is automatically reinvested at the start of the next period
• $i$ is the rate of compound interest

• The effective rate of interest for compound interest is constant

$\mathbb{R}^+$ Extension of Compound Interest

• $a$ must satisfy:

Relationship with Simple Interest

• Less if $t < 1$
• Equal if $t = 0,1$
• More if $t > 1$

Practice