Simple Interest Calculator — I = P·r·t, and what compounding adds

How it works

One multiplication and one addition: I = P·r·t, then A = P + I. The rate applies to the original principal every year, no matter how much interest has accrued — that is the defining difference from compounding, where each period's interest joins the base. The comparison table runs your exact inputs both ways, simple against annually compounded, and the third output prices the gap directly. Simple interest appears in short-term notes, some student and auto loans, and bonds' coupon arithmetic; most savings accounts and mortgages compound instead, which is what the compound-interest calculator models.

Worked example

Both cases are LibreTexts' published examples, and both render on this page. Chad's student loan — the default inputs — borrows $10,000 at 8% annual simple interest: after one year he owes 10,000 × 0.08 × 1 = $800 of interest, or $10,800 in total. Carlos's deposit — the preset — puts $20,000 at 7.25% simple interest for 6 years: 20,000 × 0.0725 × 6 = $8,700 of interest, $28,700 in total. Every other figure on the page is the same two-step arithmetic at your inputs.

Frequently asked questions

What is simple interest?

Interest charged or earned on the principal alone: I = P × r × t. A $10,000 loan at 8% simple interest costs $800 every year — the same $800 in year one and year ten, because the base never grows. The total after t years is the principal plus t years of identical interest charges.

How is it different from compound interest?

Compounding adds each period's interest to the base, so later periods earn interest on interest; simple interest never does. The two agree exactly in the first year and separate afterward — the comparison table on this page shows the gap in dollars for your own inputs, and it widens every year.

Where is simple interest actually used?

Short-term promissory notes, some auto and student loans, bond coupons (each payment is principal × coupon rate), and late-payment penalties are commonly simple. Savings accounts, credit cards, and mortgages compound — check which word your agreement uses before applying either formula.

Is simple interest better for me?

It depends which side you're on: borrowers pay less under simple interest than compounding at the same rate, and savers earn less. The gap output quantifies exactly what compounding would add on your inputs, which is the number that answers the question for your case.

How does the time factor work for partial years?

The t in P·r·t is in years, but it need not be whole: nine months is t = 0.75, and a 90-day note at a 360-day-year convention is t = 0.25 by that convention. This page uses whole years on the slider; scale the rate or principal for finer terms.

Why do my loan's numbers not match this?

Most installment loans amortize — each payment reduces the principal, so interest accrues on a falling balance rather than a fixed one. That is neither simple interest on a fixed principal nor pure compounding; the loan and amortization calculators model it.

How accurate is this, and what does it exclude?

The formula is exact for a fixed principal, fixed rate, and no payments in between. It excludes fees, payments that reduce principal mid-term, day-count conventions (360 vs 365), and taxes on earned interest. For an account that compounds, use the compound-interest calculator — at the same quoted rate it will always show more.