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Simple Interest
\( I = Prt \)

Learn how money grows over time with simple interest: understand every quantity in the formula and apply it to real-world problems.

Pre-Algebra

What Is Interest?

Interest is the cost of borrowing money or the reward for saving it. When you deposit money in a bank, the bank pays you interest. When you take out a loan, you pay interest to the lender.

Key Vocabulary

\( P \) : Principal
The original amount of money deposited or borrowed.
\( r \) : Rate
The annual interest rate, written as a decimal (e.g., 5% = 0.05).
\( t \) : Time
The number of years the money is invested or borrowed.
\( I \) : Interest
The extra money earned or owed, calculated by the formula.

Why Simple Interest Matters

Simple interest appears everywhere in daily life: savings accounts, car loans, student loans, and short-term investments. Understanding the formula helps you make smarter financial decisions.

The Simple Interest Formula

$$ I = P \cdot r \cdot t $$
Interest
Principal
Rate
Time
(rate as a decimal, time in years)

Interpreting Each Quantity

\( P \)
Principal is your starting amount: the money you put in or the size of the loan.
\( r \)
Rate tells you what fraction of the principal is earned (or charged) each year.
\( t \)
Time is how long the money stays invested or borrowed, measured in years.
\( I \)
Interest is the result: the extra dollars earned or owed.

Simple vs. Compound Interest

Simple Interest Compound Interest
Calculated on Original principal only Principal + accumulated interest
Growth pattern Linear (constant) Exponential (accelerating)
Formula \( I = Prt \) \( A = P(1+r)^t \)
Common use Short-term loans Savings, investments

Simple Interest Grows Linearly

Time (years)
Balance ($)
$500
$600
$700
$800
0
1
2
3
4
$500
$550
$600
$650
$700
+$50
+$50
+$50
+$50

How to Apply the Formula

1
Identify \( P \). Find the starting amount (principal).
2
Convert \( r \) to a decimal. Divide the percentage by 100 (e.g., \( 8\% \to 0.08 \)).
3
Determine \( t \) in years. Convert months to years if needed (e.g., 6 months = 0.5 years).
4
Multiply: \( I = P \times r \times t \).
5
Find the total if asked: \( A = P + I \).

Example 1: Savings Account

Maya deposits \$1{,}200 into a savings account that pays 4% simple interest per year. How much interest does she earn after 3 years?

\(P\) = Principal
$1,200
\(r\) = Rate
0.04
\(t\) = Time
3 years
\( I = 1{,}200 \times 0.04 \times 3 = \$144 \)

Example 2: Car Loan

Jayden borrows \$5{,}000 for a used car at 7% simple interest for 4 years. How much interest will he pay?

1
\( P = \$5{,}000 \)
2
\( r = 7\% = 0.07 \)
3
\( t = 4 \text{ years} \)
4
\( I = 5{,}000 \times 0.07 \times 4 = \$1{,}400 \)

Example 3: Time in Months

Aisha invests \$800 at 6% simple interest for 9 months. How much interest does she earn?

1
\( P = \$800 \), \( r = 0.06 \)
2
Convert months to years: \( t = \frac{9}{12} = 0.75 \text{ years} \)
3
\( I = 800 \times 0.06 \times 0.75 = \$36 \)

Solving for Other Variables

You can rearrange \( I = Prt \) to find any unknown quantity:

Find \( P \)
\( P = \frac{I}{r \times t} \)
Find \( r \)
\( r = \frac{I}{P \times t} \)
Find \( t \)
\( t = \frac{I}{P \times r} \)

Total Amount: \( A = P + I \)

\(P\) (Principal)
\(I\) (Interest)
\(A = P + I\) (Total Amount)

Common Mistakes

✕ Forgetting to Convert %
Using \( r = 5 \) instead of \( r = 0.05 \). Always divide the percentage by 100.
✕ Wrong Time Units
Plugging in months directly. Convert months to years: divide by 12.
✕ Confusing \( I \) and \( A \)
\( I \) is just the interest earned. \( A = P + I \) is the total amount.

Question 1 of 5

You deposit \$2{,}000 at 5% simple interest for 3 years. How much interest do you earn?

Question 2 of 5

In the formula \( I = Prt \), what does the variable \( r \) represent?

Question 3 of 5

Carlos borrows \$3{,}000 at 8% simple interest for 18 months. How much interest does he owe?

Question 4 of 5

You earned \$150 in simple interest on a \$2{,}500 deposit over 2 years. What was the annual interest rate?

Question 5 of 5

Lena deposits \$4{,}000 at 3.5% simple interest for 5 years. What is the total amount in her account?