Simple Interest

Sommaire

In short: Simple interest is the money earned or owed on a principal at a fixed yearly rate, calculated only on the original amount and not on earlier interest.

7th GradeRatios and Percents7.RP.A.3

What is Simple Interest?

Under simple interest, a bank account or loan charges for the use of money based on the starting amount only, so each year’s payment is identical to the one before.

The formula is $I = P \times r \times t$. Here $P$ stands for the principal in dollars, $r$ for the yearly percent written as a decimal, and $t$ for the length of time counted in years. The balance afterward is $A = P + I$.

How to spot it

A problem names a principal, an annual percent rate and a number of years or months.
The statement says interest is paid only on the original deposit or loan amount.
You are asked how much a savings account earns, or how much extra a borrower repays.
Time is given in months or days, and it must be changed into years before using the rule.

The method

List the principal $P$, convert the percent to $r$, and count the duration $t$ in whole or fractional years.
Multiply the three numbers: $I = P \times r \times t$.
Add the interest to the principal if the question asks for the final balance.
Check units: dollars for $I$, years for $t$, and a decimal rate per year.

Amber slices stack: every year adds the same $48 because only the $1,200 principal earns interest.

Simple Interest: solved example

Problem

Elena deposits $\$1{,}200$ in a credit union account paying 4% simple interest per year. How much interest does she earn in 3 years, and what is her balance?

Solution

Interest: $I = 1{,}200 \times 0.04 \times 3 = 144$ dollars.

Balance: $1{,}200 + 144 = 1{,}344$. Elena earns $\$144$ and ends with $\$1{,}344$.

Try it

Question 1

A student borrows $\$900$ at 6% simple interest for 18 months. How much interest is owed?

Show the answer

18 months is 1.5 years: $900 \times 0.06 \times 1.5 = 81$, so the interest is $\$81$.

Question 2

How long does $\$2{,}500$ take to earn $\$300$ at 3% simple interest?

Show the answer

$300 = 2{,}500 \times 0.03 \times t = 75t$, so $t = 4$ years.

Simple Interest vs. Percent Increase

A percent increase is a one-time comparison between an old value and a new value. Simple interest repeats a fixed yearly payment that grows with time, and its total depends on the number of years. Compound interest, which you meet later, differs again because earlier interest also earns interest.

Percent Increase

Keep going

Lessons

Percent Problems: Tax, Tips, Discounts and Markups

Worksheets and quizzes

Related words

Whole dictionary: A–Z · 7th Grade · Ratios and Percents

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