What's the difference between simple and compound interest?

Compound interest earns interest on the interest itself, so it grows exponentially; simple interest earns only on the principal, growing linearly. Most real bank accounts and loans use compound interest because it grows much faster over time.

Do I use the annual interest rate if time is given in months or days?

Yes, the rate r in I = Prt is always the annual rate. If you're given a monthly rate, multiply it by 12 first. Then, convert time to years: divide months by 12 or days by 365 before calculating.

Why is the interest amount so much smaller than I expected?

A common mistake is forgetting to convert percent to decimal, expecting much larger numbers. Also, simple interest grows slowly: 5% on 1000 dollars earns only 50 dollars per year. Real banks use compound interest, which grows faster.

Does simple interest ever apply to real savings accounts or credit cards?

Real banks use compound interest, which earns interest on interest. Simple Interest mainly appears in short-term loans, bond calculations, and educational contexts. It's fundamental to understanding how interest works before moving to compound interest.

Simple Interest

Simple Interest calculates the total earnings or charges on borrowed or invested money using principal, rate, and time, without compounding effects.

I = Prt

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What each symbol means

What Simple Interest takes

Symbol	Meaning
$I$	The interest earned (or charged), expressed in the same currency as the principal; confusing this with the final total amount ( $P + I$ ) makes the answer seem too small.
$P$	The principal—the starting amount of money in dollars or currency—which must be the initial amount invested or borrowed, not the ending balance.
$r$	The annual interest rate written as a decimal between 0 and 1 (such as 0.05 for 5%); forgetting to convert from percent multiplies your answer by 100.
$t$	The time period in years; if given in months, divide by 12, or if in days, divide by 365, otherwise the interest amount will be scaled incorrectly.

When to use it

Use Simple Interest when calculating earnings from savings accounts or charges from loans over a fixed period with a flat annual rate.

Level

Usually taught in: Algebra I · Appears on: SAT

Worked examples

1. Find interest earned on a savings account

Problem

You deposit 500 dollars in a savings account earning 4% annual simple interest. How much interest will you earn in 3 years?

$r = 4\% = \frac{4}{100} = 0.04$
Convert the percent to decimal form by dividing by 100.
$P = 500, \quad r = 0.04, \quad t = 3$
Identify the values: principal $P = 500$ , rate $r = 0.04$ , and time $t = 3$ years.
$I = Prt = 500 \cdot 0.04 \cdot 3$
Substitute the values into the formula $I = Prt$ .
$I = 20 \cdot 3 = 60$
Multiply: first $500 \cdot 0.04 = 20$ , then $20 \cdot 3 = 60$ .

Answer: $I = 60$

The formula $I = Prt$ calculates only the interest earned, not the total amount. After 3 years, you've earned 60 dollars in interest on your 500-dollar deposit.

2. Calculate loan interest with time given in months

Problem

A loan of 1200 dollars charges a simple interest rate of 6% per year. How much interest is owed after 18 months?

$t = 18 \text{ months} = \frac{18}{12} = 1.5 \text{ years}$
Convert time to years by dividing 18 months by 12.
$r = 6\% = 0.06$
Convert the annual rate from percent to decimal: $6\% = 0.06$ .
$P = 1200, \quad r = 0.06, \quad t = 1.5$
Identify the values: principal $P = 1200$ , rate $r = 0.06$ , and time $t = 1.5$ years.
$I = Prt = 1200 \cdot 0.06 \cdot 1.5$
Substitute into $I = Prt$ .
$I = 72 \cdot 1.5 = 108$
Multiply: $1200 \cdot 0.06 = 72$ , then $72 \cdot 1.5 = 108$ .

Answer: $I = 108$

A common error is using $t = 18$ instead of converting to years; that would give an answer 12 times too large. Always express time in years when using $I = Prt$ .

3. Find the total savings account balance after earning simple interest

Problem

Maya opens a savings account with an initial deposit of 2000 dollars at 2.5% annual simple interest. How much money will be in her account after 4 years?

$r = 2.5\% = 0.025$
Convert the rate to decimal: $2.5\% = 0.025$ .
$P = 2000, \quad r = 0.025, \quad t = 4$
Identify the values: $P = 2000$ , $r = 0.025$ , and $t = 4$ years.
$I = Prt = 2000 \cdot 0.025 \cdot 4$
Substitute into the formula.
$I = 50 \cdot 4 = 200$
Calculate: $2000 \cdot 0.025 = 50$ , then $50 \cdot 4 = 200$ .
$A = P + I = 2000 + 200 = 2200$
The final balance is the principal plus the interest earned.

Answer: $A = 2200$

The formula $I = Prt$ gives only the interest (200 dollars), not the total balance. Since the question asks for the money in the account, we must add: $A = P + I = 2200$ dollars after 4 years.

Common mistakes

Where Simple Interest usually goes wrong

The mistake	Why it is wrong	The fix
Calculating $I = 500 \times 4 \times 3 = 6000$ for a 4% rate over 3 years.	The rate was not converted from percent to decimal; using 4 instead of 0.04 multiplies the answer by 100.	Always convert: $4\% = 0.04$ . Then $I = 500 \times 0.04 \times 3 = 60$ .
An account with 500 dollars principal earning 60 dollars interest has a total of 60 dollars.	This confuses the interest ( $I$ ) with the final balance ( $A$ ); the 60 dollars is earnings alone, not the total.	The final amount is $A = P + I = 500 + 60 = 560$ dollars. Never forget to add the principal back.
Interest on 1200 dollars at 6% for 18 months is $I = 1200 \times 0.06 \times 18 = 1296$ dollars.	Time must be in years, not months; using $t = 18$ instead of $t = 1.5$ multiplies the answer by 12.	Convert to years: $t = 18 \div 12 = 1.5$ . Then $I = 1200 \times 0.06 \times 1.5 = 108$ dollars.

Tips and when to use something else

Always convert the interest rate from a percent to a decimal by dividing by 100: $5\% = 0.05$ .
Remember: the formula $I = Prt$ gives the interest earned, not the final balance. To find the total, add: $A = P + I$ .
If time is given in months, divide by 12 to convert to years; if given in days, divide by 365. The formula always uses time in years.
Use Compound Interest instead if the problem says the interest "compounds monthly" or "compounds annually"; Simple Interest assumes no reinvestment of earnings.

Related formulas

Compound InterestCompound Interest calculates how money grows when interest earns interest, used for investments, savings, and loans over time.Percent of a NumberPercent of a Number finds how much you get when taking a percentage of a quantity—essential for tips, discounts, grades, and everyday calculations.Order of OperationsOrder of Operations is the set of rules that tells you which calculation to do first when you have multiple operations in one expression.Sales Tax and TipCalculate the total final amount you pay when adding a percentage—such as sales tax or tip—to the original price of any item.Percent ChangePercent change calculates how much a quantity has increased or decreased, expressed as a percentage of its original value.

Frequently asked questions

What's the difference between simple and compound interest?: Compound interest earns interest on the interest itself, so it grows exponentially; simple interest earns only on the principal, growing linearly. Most real bank accounts and loans use compound interest because it grows much faster over time.
Do I use the annual interest rate if time is given in months or days?: Yes, the rate $r$ in $I = Prt$ is always the annual rate. If you're given a monthly rate, multiply it by 12 first. Then, convert time to years: divide months by 12 or days by 365 before calculating.
Why is the interest amount so much smaller than I expected?: A common mistake is forgetting to convert percent to decimal, expecting much larger numbers. Also, simple interest grows slowly: 5% on 1000 dollars earns only 50 dollars per year. Real banks use compound interest, which grows faster.
Does simple interest ever apply to real savings accounts or credit cards?: Real banks use compound interest, which earns interest on interest. Simple Interest mainly appears in short-term loans, bond calculations, and educational contexts. It's fundamental to understanding how interest works before moving to compound interest.

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Reviewed 2026-09-18