How the result is calculated
Simple interest is the oldest and plainest way to price money over time. You take the sum borrowed or deposited, the principal, apply the annual rate to it, and multiply by the length of time in years. The principal never changes in the calculation, so the interest for every year is the same, and interest that has built up is never itself charged interest. Compare that with compounding, where each period's interest is added to the balance and the next period's interest is worked out on the larger figure.
IP × r × t
- I
- the interest for the whole term
- P
- the principal
- r
- the annual rate as a decimal, so 5% is 0.05
- t
- the term in years
The only judgement in the formula is how to turn a term into years. A term in years needs nothing. A term in months is divided by twelve, so 18 months is 1.5 years. A term in days is divided by the number of days the agreement counts in a year, and there are two common answers. Actual/365 counts the real days in the term and divides by 365. Actual/360, the money-market convention, counts the same real days but divides by 360, which makes each day slightly more expensive. The calculator asks for the basis only when the term is in days, because a term in whole years or months is the same fraction of a year on either.
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Principal, P | $10,000.00 | Principal |
| Rate, r | 0.05 | 5% as a decimal |
| Term, t | 3 years | Term in years |
| Interest a year | $500.00 | 10,000 × 0.05 |
| Interest, I | $1,500.00 | 10,000 × 0.05 × 3 |
| Total | $11,500.00 | 10,000 + 1,500 |
Compounded once a year the same money would grow to 11,576.25, so simple interest is 76.25 lower over three years.
| Item | Amount | How it is obtained |
|---|---|---|
| Fraction of a year | 0.25 | 90 ÷ 360 |
| Interest on actual/360 | $300.00 | 20,000 × 0.06 × 0.25 |
| Fraction on actual/365 | 0.246575 | 90 ÷ 365 |
| Interest on actual/365 | $295.89 | 20,000 × 0.06 × 0.246575 |
| Cost of the 360 basis | $4.11 | 300.00 − 295.89, about 1.4% more |
Reading the result
The headline is the interest for the whole term, with the total of principal and interest beneath it. The three figures under it break the interest down: the total, the interest for one year, which is the same in every year of a simple-interest term, and the interest for one day on the basis you chose, which is the figure a lender uses to settle a loan repaid early or a deposit closed mid-term.
For terms of a year or more, the chart and table set simple interest beside the same principal compounded yearly. The two lines start together and stay close for a few years, then the compounded one curves away. The difference column is what compounding would have added: a cost to a borrower and a gain to a saver.
What changes the result
The interest is directly proportional to each of the three inputs. Double the principal, the rate or the term and the interest doubles, which is what makes simple interest easy to check by hand and easy to compare.
The day count changes the result only for a term in days, and only a little, but it is a real difference in what you pay. Over a full calendar year an actual/360 agreement charges 365/360 of its quoted rate, so a loan quoted at 5% costs about 5.07% a year. On a large or long commercial loan that is worth reading the agreement for.
The term unit matters for how you enter a part period. Six months is exactly half a year in months, but 182 days on actual/365 is slightly less than half, and 183 days slightly more. A lender that accrues daily uses the days.
What is not included
The calculation assumes the principal stays outstanding for the whole term. A loan repaid in instalments is not a simple-interest calculation of this kind: interest is charged on a falling balance, and the loan or EMI calculators handle that. Fees, arrangement charges and insurance are not interest and are not included; the APR calculator shows what they do to the true cost of a loan.
Tax on interest a saver earns is not deducted, and a calendar with a leap year is not modelled: a term in days is divided by the basis you choose, which is how most agreements state it.
Using the result
Use simple interest to check a quote or a statement for anything that accrues interest without adding it to the balance: a short-term loan, a bill, a deposit that pays its interest out, or the interest for a part period on almost any product. Multiply the daily figure by the days and you have the amount a lender should charge or a bank should pay.
When you compare offers, make sure they are on the same footing. A simple rate and a compound rate of the same headline percentage are not the same price over more than a year, and two simple rates on different day counts are not quite the same price either.