Simple interest is one of 3 finance formulas in the arithmetic section of this library, and it is used at middle school · high school level.
Why simple interest works
Simple interest pays the same amount every year because it is always figured on the original deposit and never on the interest already earned. One year at 5 percent on 1000 dollars pays 50 dollars, so three years pays three of those. Multiplying by t is just stacking identical yearly payments.
What each symbol means
$P$ is principal, $r$ is the decimal annual rate, $t$ is years, $I$ is interest, and $A$ is total.
Simple interest: when it holds
The rate and time unit must agree; this model does not compound interest.
When it stops applying
It does not describe accounts that pay interest on interest, which is most of them. Over 10 years at 5 percent, simple interest pays 500 dollars on 1000, while interest compounded yearly pays 628.89, and the gap widens every year after that.
Simple interest: a worked example
$P=1000$, $r=0.05$, $t=3$ gives $I=150$ and $A=1150$.
The mistake to avoid
What people do: Students type the rate as the whole number 5 instead of the decimal 0.05.
Why it goes wrong: That multiplies the interest by 100. On a 1000 dollar deposit for 3 years it produces 15,000 dollars of interest, more than ten times the money that was deposited.
Do this instead: Divide the percent by 100 before it goes into the formula: 5 percent is 0.05, so 1000 times 0.05 times 3 is 150 dollars of interest and a total of 1150.
Simple interest: step by step
- Name the unknown, and the unit the answer has to come out in.
- Match the symbols to your values. $P$ is principal, $r$ is the decimal annual rate, $t$ is years, $I$ is interest, and $A$ is total.
- Check the conditions before substituting. The rate and time unit must agree; this model does not compound interest.
- Substitute, keep exact values to the last line, then test the sign, size, and unit against a rough estimate — the check that catches most arithmetic slips.
Where this formula fits
- Subject
- Arithmetic formulas — 13 entries in this library
- Topic
- Finance
- Level
- Middle school · High school
Formulas are easiest to keep when they sit inside a method rather than on a list. Use the links below to see where simple interest comes from, to check a calculation against a tool, and to practise it until you can recall it without looking.
- Exponentials and Logarithms — the lesson behind this formula: move between growth models and inverse logarithmic form.
- Arithmetic Calculator — check your substitution and the value it produces.
- Study arithmetic — the subject guide that explains the ideas these formulas compress.
- Arithmetic Practice — questions that make you retrieve the formula instead of recognising it.
- All 13 arithmetic formulas — the full grouped reference, or the complete formula library.
Questions about simple interest
What if the loan is for a number of months?
Turn the months into years, since the rate is an annual one. Nine months is 0.75 of a year, so t goes in as 0.75 rather than 9.
Is A always equal to P plus I?
Yes, and that is where the second formula comes from. Factoring P out of P + Prt leaves P(1 + rt), so the two lines say the same thing in different shapes.
Where is simple interest actually used?
Mostly in short-term loans, car finance, and some bonds that pay a fixed coupon. It is also the standard model in classrooms because the arithmetic stays clean.
How do I find the rate if I know the interest?
Divide the interest by P times t. Earning 150 dollars on 1000 dollars over 3 years gives 150/3000 = 0.05, which is 5 percent a year.