Simple interest is interest paid only on the original amount of money, called the principal, at a fixed yearly rate. Find it with I = Prt: multiply the principal by the rate written as a decimal and by the time in years. The interest is the same every year, so the balance grows in a straight line.
With simple interest only the principal earns interest, so every year adds the same amount and the balance climbs in a straight line.
Formal definition and notation
For a principalP invested or borrowed at an annual interest rate r (a decimal) for t years, the simple interest is I = Prt. Interest is never added to the principal before the next period, so each year earns the same amount, Pr. The total amount, or future value, is A = P + I = P(1 + rt), a linear function of time.
Symbol
Read it as
Meaning
I
I
the interest, in money
P
P
the principal, the amount first deposited or borrowed
r
r
the annual rate as a decimal: 6% is 0.06
t
t
the time in years
A
A
the total amount at the end, P + I
Key facts
Change the percent to a decimal first: 4% becomes 0.04, and 2.5% becomes 0.025.
Each year earns the same interest, P × r. Doubling the time doubles the interest.
The balance A = P(1 + rt) grows by equal steps, so its graph against time is a straight line with slopePr.
“Interest” asks for I only; “total”, “balance” or “amount owed” asks for A = P + I.
You can solve I = Prt for any letter: r = IPt, t = IPr, P = Irt.
Simple interest formula
Simple interest formula
I = Prt and A = P + I
P
principal (starting amount)
r
yearly rate as a decimal (5% = 0.05)
t
time in years (18 months = 1.5 years)
A
total paid back or saved
Match the units: a yearly rate needs the time in years. Divide months by 12 before you multiply.
Try it: interest grows with time
Interactive
This table uses 900 dollars at 4% a year, which earns 36 dollars each year. Change the interest per year and watch every row scale by the same factor: interest is proportional to time.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Simple Interest examples, step by step
Example 1: Interest for whole years
Warm-up
Find the simple interest on 600 dollars at 4% per year for 3 years.
Write the rate as a decimal: 4% = 0.04.
Use I = Prt: I = 600 × 0.04 × 3.
600 × 0.04 = 24 per year, and 24 × 3 = 72.
Answer: The interest is 72 dollars.
Example 2: Time given in months
Core
Jada borrows 2,400 dollars at 6.5% simple interest for 18 months. How much interest does she pay, and what is the total she pays back?
Change months to years: t = 1812 = 1.5.
Rate as a decimal: 6.5% = 0.065.
I = 2400 × 0.065 × 1.5 = 156 × 1.5 = 234.
Total: A = 2400 + 234 = 2634.
Answer: She pays 234 dollars of interest, so she pays back 2,634 dollars in all.
Example 3: Work backward to the rate
Test-style
A savings account pays simple interest. A deposit of 1,500 dollars earns 135 dollars of interest in 3 years. What is the annual interest rate?
Start from I = Prt and solve for r: r = IPt.
r = 1351500 × 3 = 1354500.
1354500 = 0.03, and 0.03 = 3%.
Answer: The annual rate is 3%.
Common mistakes
✗ MistakeUsing the percent as a whole number: 600 × 4 × 3 = 7,200 dollars of interest.
Compound interest is added to the balance, and later interest is figured on the bigger balance, so the growth curves upward. 1,000 dollars at 5% for 2 years earns 100 dollars simple, but 102.50 dollars compounded yearly.
Simple Interestvs.Interest rate
The rate r is a percent per year, such as 5%. The interest I is an amount of money, such as 50 dollars.
Quick check: 3 questions
Question 1 of 3
How much simple interest does 1,000 dollars earn at 5% per year for 2 years?
Show answer and explanation
Answer: C.I = 1000 × 0.05 × 2 = 100 dollars. 10,000 comes from using 5 instead of 0.05, 1,100 is the total A, not the interest, and 102.50 is compound interest.
Question 2 of 3
What is the simple interest on 300 dollars at 8% per year for 6 months?
Show answer and explanation
Answer: A. Six months is 0.5 year: 300 × 0.08 × 0.5 = 12. 144 used t = 6, 24 is a full year of interest, and 312 is the total.
Question 3 of 3
Which formula gives the total amount after t years of simple interest?
Show answer and explanation
Answer: D.A = P + Prt = P(1 + rt). Prt is only the interest, P(1 + r)t is the compound interest formula, and adding P + r + t mixes money, a rate and years.
Simple Interest: frequently asked questions
What does each letter in I = Prt mean?
I is the interest earned or owed, P is the principal (the money you start with or borrow), r is the yearly interest rate written as a decimal, and t is the time in years. For 500 dollars at 3% for 4 years, I = 500 × 0.03 × 4 = 60 dollars.
How do you find simple interest for months or days?
Turn the time into years first, because the rate is per year. Divide months by 12: 9 months is 912 = 0.75 year. For days, divide by the number of days the lender uses for a year, usually 365. Then use I = Prt as usual.
Is simple interest or compound interest better?
It depends on which side you are on. When you save, compound interest earns more over time, because interest also earns interest. When you borrow, simple interest costs less at the same rate. For one year with yearly compounding, both give the same interest.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.RP.A.3
Cite this entry
Effortless Math Team. “Simple Interest.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/simple-interest/
Flashcard
TermSimple InterestI = Prt
DefinitionInterest on the starting amount only: principal times yearly rate times years. 600 dollars at 4% for 3 years earns 600 × 0.04 × 3 = 72 dollars.
PrincipalThe principal is the original amount of money that is borrowed, deposited or invested, before any interest is added. In the simple interest formula I = Prt, the letter P stands for the principal. Deposit 2,000 dollars at 3% simple interest for 4 years: the principal is 2,000 dollars, the interest is 240 dollars, and the total is 2,240 dollars.Problem Solving · Grade 7, Algebra 1PeriodThe period of a repeating function is the horizontal length of one complete cycle: the smallest distance after which the graph repeats exactly. y = sinx and y = cosx have period 2π, or 360°, and y = tanx has period π. For y = sin(Bx) or y = cos(Bx), the period is 2π|B|.Trigonometry · Algebra 2, PrecalculusLinear FunctionA linear function is a function whose graph is a straight line. You can write it as f(x) = mx + b, where m is the slope, or constant rate of change, and b is the y-intercept. Each time x increases by 1, the output changes by the same amount, m.Functions · Grade 8, Algebra 1PercentA percent is a number out of 100. Percent means per hundred, so 25% means 25 out of 100, or 25100 = 0.25. To find a percent of a quantity, change the percent to a decimal and multiply: 20% of 80 is 0.20 × 80 = 16. The symbol for percent is %.Number System · Grade 5, Grade 6, Grade 7SlopeSlope is a number that measures how steep a line is: the change in y divided by the change in x between any two points on the line, often called rise over run. A positive slope rises from left to right, a negative slope falls, and a horizontal line has slope 0.Algebra · Grade 8, Algebra 1Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5Compound InterestCompound interest is interest computed on the principal plus all the interest already earned, so the balance grows exponentially. The formula is A = P( 1 + rn )nt, where P is the principal, r the annual rate, n the compoundings per year and t the years. It beats simple interest after the first period.Functions · Grade 7, Algebra 1, Algebra 2NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2RateA rate is a ratio that compares two quantities measured in different units, such as 150 miles in 3 hours or 12 dollars for 4 pounds. The word “per” signals a rate. Dividing gives the unit rate, the amount for 1 unit: 150 miles in 3 hours is 50 miles per hour.Ratios and Proportions · Grade 6, Grade 7DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6Exponential GrowthExponential growth is an increase by the same percent, or the same factor, in each equal time period, so the amount grows faster and faster. It is modeled by y = a(1 + r)t, where a is the starting amount and r is the growth rate. Growing 10% a year multiplies the amount by 1.1 every year.Functions · Algebra 1, Algebra 2Percent IncreasePercent increase is how much a quantity grew, written as a percent of its original value. Subtract the original from the new value, divide by the original, and multiply by 100: from 80 to 100 is 2080 = 25%. To increase a number by r%, multiply it by 1 + r100, so 80 × 1.25 = 100.Ratios and Proportions · Grade 7, Grade 8, Algebra 1FormulaA formula is a rule written with symbols that shows how quantities are related. It is an equation with two or more variables, such as A = lw for the area of a rectangle. Formulas help solve problems the same way each time: substitute the values you know, then compute the one you need.Problem Solving · Grade 5, Grade 6, Grade 7