Simple Interest

💰 Simple Interest

Part 1 of 5 — Concept Introduction

When you put money in a savings account, the bank pays you a little extra for letting them hold it. When you borrow money, you pay a little extra back for the right to use it. That "little extra" is called interest.

Interest is the cost of borrowing money, or the reward for saving money.

Simple interest is the easiest kind to calculate. It is figured only on the original amount of money — the part you started with — and never on the interest itself.

The Four Key Words 🔑

Every simple-interest problem is built from four ideas:

Symbol	Name	What it means
$P$	Principal	The original amount borrowed or invested
$r$	Rate	The yearly percent of interest, written as a decimal
$t$	Time	The length of time, measured in years
$I$	Interest	The extra money earned or owed

Once you know the principal, rate, and time, you can find the interest.

The Simple Interest Formula

Everything comes down to one short formula:

$I = P \times r \times t$

We usually just write it as $I = Prt$.

• $I$ = interest earned or paid
• $P$ = principal (the starting amount)
• $r$ = rate as a decimal (so $5\% = 0.05$)
• $t$ = time in years

⚠️ Turn the percent into a decimal first!

The rate is given as a percent, but the formula needs a decimal. To convert, divide the percent by $100$ (move the decimal point two places to the left):

• $4\% = 0.04$
• $6\% = 0.06$
• $18\% = 0.18$

Finding the Total Amount

After you find the interest, the total amount of money is just the principal plus the interest:

$A = P + I$

So if you invest $500 and earn $60 in interest, you end up with $A = 500 + 60 = 560$, i.e. $560.

Worked Example 🧮

You invest $500 at $4\%$ simple interest for $3$ years. How much interest will you earn?

• $P = 500$, $\quad r = 0.04$, $\quad t = 3$

$I = Prt = 500 \times 0.04 \times 3 = 500 \times 0.12 = 60$

You earn $60 in interest, and your total amount is $500 + 60 = 560$, i.e. $560.

Concept Check 🎯

Let's make sure the key ideas are clear before we calculate.

📝 Worked Examples

Part 2 of 5 — Worked Examples

Let's walk through two problems slowly. Every problem follows the same three steps.

Step 1: Change the rate from a percent to a decimal. Step 2: Plug $P$, $r$, and $t$ into $I = Prt$. Step 3: Multiply, then (if asked) add the interest to the principal.

Example 1: A Loan 🏦

Maria borrows $1,200 at $6\%$ simple interest for $2$ years. How much interest will she owe, and how much must she repay in total?

Step 1 — Rate to decimal: $6\% = 0.06$.

Step 2 — Use the formula:

$I = Prt = 1200 \times 0.06 \times 2$

$I = 1200 \times 0.12 = 144$

Step 3 — Total to repay:

$A = P + I = 1200 + 144 = 1344$

Maria owes $144 in interest and repays $1,344 in all. ✅

Example 2: A Savings Account 🌱

You invest $800 at $5\%$ simple interest for $4$ years. How much interest do you earn?

• $P = 800$, $\quad r = 0.05$, $\quad t = 4$

$I = Prt = 800 \times 0.05 \times 4 = 800 \times 0.20 = 160$

You earn $160 in interest, for a total of $800 + 160 = 960$, i.e. $960. 🎉

Your Turn 🧮

You invest $2,000 at $3\%$ simple interest for 5 years. Work through it one step at a time.

1. Write the rate $3\%$ as a decimal. (Type it like $0.05$.)

2. Find the interest $I = Prt$. (Type just the number of dollars, like $150$.)

3. Find the total amount $A = P + I$. (Type just the number of dollars.)

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Use $I = Prt$ for each problem. Remember: change the percent to a decimal first.

Match the Pieces 🔍

A problem says: "You invest $600 at $5\%$ simple interest for $4$ years." Pick the correct value for each part of the formula.

🌍 Application & Word Problems

Part 4 of 5 — Real-World Problems

In real life, time is not always a whole number of years. The formula $I = Prt$ needs $t$ in years, so you often have to convert.

Converting Time to Years ⏳

You are given	Convert by	Example
Months	months $\div\, 12$	$6$ months $= \frac{6}{12} = 0.5$ years
Months	months $\div\, 12$	$9$ months $= \frac{9}{12} = 0.75$ years
Days	days $\div\, 365$	$180$ days $= \frac{180}{365}$ years

Credit Card Example 💳

A credit card charges $18\%$ annual simple interest. If you carry a $300 balance for 6 months, how much interest builds up?

Step 1 — Convert time: $6$ months $= \frac{6}{12} = 0.5$ years.

Step 2 — Use the formula:

$I = Prt = 300 \times 0.18 \times 0.5 = 300 \times 0.09 = 27$

You would owe an extra $27 in interest after 6 months. That is why paying off cards quickly matters! 💡

Real-World Practice 🧮

You invest $800 at $5\%$ simple interest for 9 months. Work it out step by step.

1. Convert $9$ months to years as a decimal. (Type it like $0.5$.)

2. Find the interest $I = Prt$. (Type just the number of dollars, like $30$.)

3. Find the total amount $A = P + I$. (Type just the number of dollars.)

Word Problem Check 🎯

Read carefully — watch the units!

🏆 Review & Challenge

Part 5 of 5 — Putting It All Together

You've learned the whole simple-interest toolkit. Here is everything in one place:

Idea	Formula / Rule	Remember
Interest	$I = Prt$	The main formula
Total amount	$A = P + I$	Principal plus interest
Percent → decimal	divide by $100$	$5\% = 0.05$
Months → years	divide by $12$	$6$ mo $= 0.5$ yr
Days → years	divide by $365$	$180$ days $= \frac{180}{365}$ yr

The Three-Step Habit ✅

1. Change the rate to a decimal.
2. Make sure time $t$ is in years.
3. Multiply $P \times r \times t$, then add to $P$ if you need the total.

Master these, and you can handle any simple-interest problem — savings, loans, or credit cards. Now try the challenge below! 💪

Challenge Round 🎯

These problems mix everything together. Take your time and check your units.