Simple Interest — I can compute simple interest and...

SECTION 1

Where Did Interest Come From?

Have you ever lent a friend something and expected a little extra back? That idea is actually thousands of years old. Interest is the extra money a borrower pays for using someone else's money. People have been charging interest since the very first civilizations.

Ancient farmers in Mesopotamia borrowed seeds and paid back more seeds after the harvest. Over time, people started lending money instead of seeds. Rules about how much extra to charge were written into some of the earliest laws ever recorded.

2000 BCE

Mesopotamian Grain Loans

Farmers in ancient Sumer borrowed grain and repaid extra after the harvest. This was one of the earliest forms of interest.

1754 BCE

Code of Hammurabi

King Hammurabi of Babylon wrote laws that set maximum interest rates. This is one of the oldest legal documents in history.

300 BCE

Greek and Roman Banking

Banks in ancient Greece and Rome lent money to merchants and governments. Interest helped fund trade across the Mediterranean Sea.

1200s CE

European Trade Boom

Italian merchants developed modern banking. They used simple interest formulas that look very similar to the one you will learn today.

Today

Modern Savings & Loans

Banks, credit cards, and car loans all use interest. Understanding the formula helps you make smart money decisions.

So here is the big question: if you put $200 in a savings account that pays 5% per year, how much extra money do you earn after 3 years? That is exactly the kind of problem the simple interest formula was built to answer.

SECTION 2

Core Principles & Key Definitions

Before we dive into calculations, let's make sure you know the four key quantities in the formula. Each letter stands for a real-world idea that connects to money and time.

I — Interest

The extra money earned (on savings) or owed (on a loan). This is what you are solving for most of the time.

P — Principal

The starting amount of money. If you deposit $500, then P = 500. Think of it as the original amount before any interest is added.

r — Rate

The interest rate per year, written as a decimal. For example, 5% becomes 0.05. Always convert the percent before plugging it in!

t — Time

The number of years the money is borrowed or invested. If the rate is per year, then time must also be in years.

✦ KEY TAKEAWAY

Think of simple interest like renting a bicycle. The principal (P) is the bike itself. The rate (r) is how much you pay per hour. The time (t) is how many hours you keep it. Multiply the rental price by the number of hours and you get the total rental fee — that's the interest (I).

SECTION 3

Seeing Simple Interest Grow

The diagram below shows what happens when you deposit $200 at a 5% annual rate. Each year, you earn the same amount of interest — $10. That steady, equal growth is what makes it simple interest.

Each bar shows the total amount after that many years. The purple section represents the original principal ($200). The cyan growth shows the accumulated interest. Notice that each year adds exactly $10 — simple interest grows in a straight line.

Look at the yellow "+$10" labels. The interest earned each year is the same. That happens because simple interest is always calculated on the original principal, not on the growing total. The bars go up like steps of equal height — a straight-line pattern.

SECTION 4

The Simple Interest Formula

Now let's look at the formula itself. It has only three things to multiply together, making it one of the most useful formulas you will learn in pre-algebra.

SIMPLE INTEREST FORMULA

I = P × r × t

I = interest earned or owed (in dollars) • P = principal, the starting amount (in dollars) • r = annual interest rate (as a decimal) • t = time (in years)

⚠️ Don't Forget!

The rate must be a decimal, not a percent. To convert, divide the percent by 100. For example, 8% → 8 ÷ 100 = 0.08. If you leave it as 8, your answer will be 100 times too big!

TOTAL AMOUNT (PRINCIPAL + INTEREST)

A = P + I

A = total amount in the account after earning interest. You find the interest first, then add it back to the principal.

Here is a quick example with numbers. Suppose P = $200, r = 5% = 0.05, and t = 3 years.

SUBSTITUTION EXAMPLE

I = 200 × 0.05 × 3 = 30

The interest earned is $30. The total amount in the account would be A = 200 + 30 = $230.

SECTION 5

Breaking Down Each Quantity

Let's zoom in on each piece of the formula. The diagram below shows how each quantity connects to a real-world meaning and what units it uses.

This diagram maps each letter in I = P × r × t to its meaning, unit, and a sample value. The three quantities flow down into the result box where they are multiplied together.

Summary of quantities in the simple interest formula

Quantity	Letter	Unit	What to Ask Yourself
Interest	I	Dollars ($)	How much extra money is earned or owed?
Principal	P	Dollars ($)	How much money did I start with?
Rate	r	Decimal	What percent does the bank pay per year? (Convert to decimal!)
Time	t	Years	How many years is the money saved or borrowed?

💡 What If Time Is in Months?

If a problem says "6 months," convert to years first. Since there are 12 months in a year, 6 months = 6 ÷ 12 = 0.5 years. Always match the time unit to the rate unit. If the rate is "per year," the time must be in years.

SECTION 6

Worked Example: Saving for a New Bike

Maya deposits $600 into a savings account that earns 4% simple interest per year. She plans to leave the money there for 2.5 years. How much interest will she earn, and what will her total balance be?

Maya's Savings Account

Step 1 — Identify the Given ValuesRead the problem carefully and match each number to a letter. P = $600 (the deposit), r = 4% (the annual rate), t = 2.5 years.

P = 600, r = 4%, t = 2.5

Step 2 — Convert the Rate to a DecimalDivide the percent by 100. So 4% ÷ 100 = 0.04. This is a critical step — if you skip it, your answer will be way too large.

r = 0.04

Step 3 — Substitute into the FormulaWrite the formula and plug in the values: I = P × r × t = 600 × 0.04 × 2.5.

I = 600 × 0.04 × 2.5

Step 4 — Multiply Step by StepFirst multiply 600 × 0.04 = 24. Then multiply 24 × 2.5 = 60. Take it one multiplication at a time so you don't make errors.

I = $60

Step 5 — Find the Total AmountAdd the interest to the principal to find the total balance: A = P + I = 600 + 60 = 660.

A = $660

Maya earns $60 in interest over 2.5 years, bringing her total to $660. Notice that she earned money just by leaving it in the bank. That is the power of interest!

SECTION 7

Two Sides of Interest: Saving vs. Borrowing

Interest works both ways. When you save money, interest is your friend — the bank pays you. When you borrow money, interest is a cost — you pay the bank. The formula is the same either way, but the meaning changes.

Saving vs. borrowing: same formula, different perspective

Feature	Saving (Depositing)	Borrowing (Loan)
Who earns interest?	You earn interest from the bank.	The bank earns interest from you.
Is interest good or bad for you?	Good — your money grows!	Bad — you owe extra money.
What does P represent?	The amount you deposited.	The amount you borrowed.
Total amount (A = P + I)	How much is in your account.	How much you must pay back.
Want higher r?	Yes! Higher rate = more money for you.	No! Higher rate = more money you owe.

✦ KEY TAKEAWAY

Imagine you and a friend both use the same recipe for lemonade. One of you sells it and earns money; the other drinks it and spends money. The recipe (formula) is the same — I = P × r × t — but whether interest helps or hurts depends on which side of the deal you are on.

SECTION 8

Looking Ahead: Simple vs. Compound Interest

Simple interest is a great starting point, but most real-world bank accounts use compound interest. With compound interest, you earn interest on your interest — your money grows faster over time. You will study this in future math courses.

Simple interest vs. compound interest at a glance

Feature	Simple Interest	Compound Interest
Interest calculated on	The original principal only	The principal plus previously earned interest
Growth pattern	Straight line (same amount each year)	Curve (grows faster and faster)
Formula	I = P × r × t	A = P(1 + r)ᵗ (you'll learn this later!)
Typical use	Car loans, short-term loans	Savings accounts, credit cards

For now, mastering simple interest gives you the foundation. Once you understand I = P × r × t, compound interest will feel like a natural next step. Think of simple interest as learning to walk before you run!

SECTION 9

Practice Problems

Try these five problems on your own. They start easy and get harder. Remember: convert the rate to a decimal, plug into I = P × r × t, and multiply step by step.

PROBLEM 1 — CONCEPTUAL

In the formula I = P × r × t, what does the letter P stand for? Explain in your own words why P matters when calculating interest.

PROBLEM 2 — BASIC CALCULATION

Find the simple interest on $400 at a rate of 3% per year for 5 years.

PROBLEM 3 — INTERMEDIATE

Carlos borrows $1,200 at 6% simple interest per year. He pays it back after 18 months. How much total does Carlos pay back?

PROBLEM 4 — APPLIED

Aisha earns $135 in simple interest after keeping $900 in a savings account for 3 years. What is the annual interest rate? Give your answer as a percent.

PROBLEM 5 — CRITICAL THINKING

Two friends each deposit money at 4% simple interest per year. Javier deposits $800 for 2 years. Kim deposits $400 for 4 years. Who earns more interest? Explain why, and discuss what this tells you about the relationship between P, t, and I.

SUMMARY

Lesson Summary

Simple interest is calculated using the formula I = P × r × t, where I is the interest earned or owed, P is the principal (starting amount), r is the annual rate as a decimal, and t is the time in years. Always convert the percent to a decimal before substituting. Interest grows in a straight-line pattern because it is always calculated on the original principal, not on the growing total.

The formula works for both saving (where interest is money you earn) and borrowing (where interest is money you owe). You can rearrange the formula to solve for any missing variable — P, r, or t — by dividing. Simple interest is the foundation for understanding compound interest, which you will study in later courses. Master I = P × r × t now, and you'll be ready for more advanced financial math!