Simple Interest
Fractions & DecimalsSimple 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, called the principal. It is calculated by multiplying the principal by the rate and the time.
Example
You deposit $\$500$ in a bank account with $4\%$ simple interest per year for $3$ years. Interest $= \$500 \times 0.04 \times 3 = \$60$. Total after $3$ years $= \$500 + \$60 = \$560$.
Key Insight
Simple interest is "simple" because it only looks at the original amount, never the interest that has already been earned. It grows in a straight line - add the same amount each year.
Definition
Simple interest $I = Prt$, where $P$ is the principal, $r$ is the annual interest rate (as a decimal), and $t$ is the time in years. The total amount $A = P + I = P(1 + rt)$. Simple interest grows linearly with time. Loans for cars and short-term borrowing often use simple interest.
Example
A $\$2{,}000$ loan at $6\%$ simple interest for $2.5$ years. $I = 2000 \times 0.06 \times 2.5 = \$300$. Total owed $= \$2{,}300$. Monthly payment $= \$2{,}300/30$ months $\approx \$76.67$.
Key Insight
Simple interest is fair for short periods because you pay only for what you borrow. Over long periods, compound interest produces much more growth. The difference between $A = P(1+rt)$ (linear) and $A = P(1+r)^t$ (exponential) widens dramatically over decades.
Definition
Simple interest represents linear growth: $A(t) = P(1 + rt)$, a first-degree polynomial in $t$ with slope $Pr$. This is the first-order Taylor approximation of compound interest $A(t) = P(1+r)^t$ at $t=0$: $(1+r)^t \approx 1 + rt$ for small $t$. The ODE for simple interest is $dA/dt = Pr$ (constant rate), versus $dA/dt = rA$ (proportional to current value) for compound interest.
Example
The "Rule of 72" approximates doubling time for compound interest: $t \approx 72/r\%$. For simple interest, exact doubling time: $2P = P(1+rt)$ gives $t = 1/r$. At $r=6\%$, $t=1/0.06 \approx 16.7$ years (simple) vs. $72/6 = 12$ years (compound) - compound doubles faster.
Key Insight
The distinction between linear (simple) and exponential (compound) growth is one of the most consequential mathematical facts for personal finance. 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 (simple) model most people implicitly assume.