Last updated: 2026-05-09

Simple interest defined

Simple interest is interest computed only on the original principal, at a fixed rate, for the length of the term: $I = P \cdot r \cdot t$. The interest earned in one period is never added to the principal, so the balance that interest is charged on stays constant and the interest accumulates in a straight line rather than accelerating over time.

The formula

Simple interest is linear in both rate and time:

Total amount (principal plus interest):

Compound interest, even at the simplest annual-compounding frequency, breaks the linearity:

The two formulas agree at $t = 0$ and at $t = 1$ year (since $(1+r)^1 - 1 = r$). After that they diverge — slowly at first, then more widely.

Why the gap widens

In year 1 the interest is the same under both methods. In year 2, the compounding method adds the first year's interest to the principal before charging the rate, so interest is computed on $P + r \cdot P$ instead of just $P$. Each year's interest contribution is applied to the growing balance — the geometric expansion that drives long-horizon savings growth and long-horizon debt accumulation.

$10,000 at 6% for various horizons:

Over 30 years compound interest is 2.6× the simple interest figure on the same principal and rate.

When simple interest is actually used

Three real-world cases:

1. Short-term Treasury bills and commercial paper. T-bills under one year quote a discount yield that is effectively a simple-interest rate. The difference versus compounding is genuinely small at those horizons.
2. Some private and intra-family loans. When the parties agree on "simple interest," the calculation is exactly $I = P \cdot r \cdot t$ and no compounding ever occurs.
3. Educational contexts. Almost every textbook introduces simple interest first because it is mechanically easier to follow, which makes compound interest read as the natural next step rather than a separate concept.

For everything else — savings accounts, mortgages, student loans, auto loans, credit cards — assume compounding (usually monthly) unless the contract specifies otherwise.

Time units

The term can be entered in days, months, or years, matched to the product being modelled: a 90-day Treasury bill as 90 days, a 6-month certificate of deposit as 6 months, a 5-year savings deposit as 5 years. The calculator canonicalises the entry to years before evaluating, so the result is identical regardless of which unit is chosen — the unit toggle only sets which number is convenient to type.