What is simple interest?

Three inputs drive it: the principal, the annual rate as a decimal, and the time in years. Multiply the three for the interest, then add the principal for the total payable. Partial years are just fractions, so nine months is 0.75 of a year, and 45 days on an actual-days basis is roughly 0.1233 of one.

Day-count conventions matter more than they look. Some contracts count actual days over 365, others use a 30/360 convention, and on a large principal over a short period that choice moves the number. Check which one the contract specifies, and make sure the rate you are given is stated per annum before you use it.

Simple interest turns up on short-term promissory notes and bills of exchange, on short-term trade credit and vendor terms where the charge is fixed and does not compound, and on fixed-term arrangements that say so explicitly in the product terms. Some loan and lease contracts calculate on the original amount too, though most vehicle and equipment finance uses a reducing balance or a more involved structure.

Most consumer loans and mortgages do not use it. They charge on the balance still outstanding and compound anything unpaid. Applying the simple formula to an amortising loan gives the wrong answer, so work from the repayment schedule instead.

Compound interest is charged on the principal plus the interest already accrued, so once a compounding period has passed it ends up ahead of simple interest, and the gap widens as the rate, the time and the compounding frequency rise. Simple interest keeps the charge tied to the original amount, which is what makes it predictable.

A flat rate quote looks similar but behaves differently. It applies a percentage to the original principal for the whole term while your repayments are bringing the balance down, which understates the real cost. To compare properly, convert both to an annual cost figure, or lay two amortisation schedules side by side.