Simple Interest
Simple interest is interest calculated only on the original principal amount, not on previously earned interest.
Formula
I = Prt
Definition
Simple interest is the extra money you earn (or pay) based only on the original amount of money, the principal, never on interest already earned; it is calculated by multiplying the principal by the rate and the time. Formally, $I = Prt$, where $P$ is the principal, $r$ the annual rate (as a decimal), and $t$ the time in years, giving a total amount $A = P + I = P(1 + rt)$ that grows linearly over time. This linear growth is the first-order Taylor approximation of compound interest at $t=0$, since $(1+r)^t \approx 1 + rt$ for small $t$; the underlying differential equation is $dA/dt = Pr$ (a constant rate), in contrast to $dA/dt = rA$ (proportional to the current value) for compound interest.
Example
Depositing $\$500$ at $4\%$ simple interest for $3$ years earns $\$500 \times 0.04 \times 3 = \$60$, for a total of $\$560$. A $\$2{,}000$ loan at $6\%$ simple interest for $2.5$ years accrues $2000 \times 0.06 \times 2.5 = \$300$ in interest, for a total owed of $\$2{,}300$. The exact doubling time for simple interest solves $2P = P(1+rt)$, giving $t = 1/r$; at $r=6\%$, that is $t \approx 16.7$ years, compared to the Rule of 72's estimate of $72/6 = 12$ years for compound interest, showing compound interest doubles much faster.
Key Insight
Simple interest is "simple" because it only looks at the original amount, never the interest already earned, so it grows in a straight line, the same amount added each year. This makes it fair for short borrowing periods, but over long periods compound interest produces much more growth, and the gap between $A = P(1+rt)$ (linear) and $A = P(1+r)^t$ (exponential) widens dramatically over decades. Albert Einstein allegedly called compound interest the "eighth wonder of the world," a reflection of how profoundly counterintuitive exponential growth is compared to the linear model most people implicitly assume.