Simple Interest

Simple interest is calculated only on the amount you started with.

I = P × r × t, where P is the starting amount, r is the yearly rate as a decimal, and t is time in years.

Borrow $2,000 at 5% for 3 years: I = 2000 × 0.05 × 3 = $300 interest, so you repay $2,300.

Watch the units. If a rate is per year, t must be in years. Six months is t = 0.5, not 6.

Simple interest grows linearly. The total value is

A = P + Prt = P(1 + rt)

which is a linear function of t with slope Pr. Graphed against time it is a straight line.

Compound interest instead applies the rate to the accumulated balance, giving A = P(1 + r/n)^{nt} for n compounding periods per year — an exponential function, and the subject of a full topic in Algebra 2. Over one year at one compounding period the two agree exactly; beyond that, compounding always yields more, and the gap widens with time.

Because A = P(1 + rt) is linear, any one of the four variables can be isolated by ordinary algebra, which makes simple interest a standard example when literal equations are introduced.