Simple Interest

What is Interest?

Interest is money paid for borrowing money OR money earned for saving/lending money.

When you borrow: You pay interest to the lender When you save: You earn interest from the bank

Simple Interest Formula

I = PRT

Where:

• I = Interest (amount earned or paid)
• P = Principal (starting amount)
• R = Rate (interest rate as a decimal)
• T = Time (in years)

Note: Always convert percent to decimal for R!

Calculating Simple Interest

Example 1: Savings Account

You deposit $500 at 3% annual interest for 2 years. How much interest do you earn?

Given:

• P = $500
• R = 3% = 0.03
• T = 2 years

Formula: I = PRT

Calculate: I = 500 × 0.03 × 2 = 30

Answer: $30 interest earned

Total amount after 2 years: $500 + $30 = $530

Example 2: Loan

You borrow $1,000 at 5% annual interest for 3 years. How much interest will you pay?

Given:

• P = $1,000
• R = 5% = 0.05
• T = 3 years

Calculate: I = 1,000 × 0.05 × 3 = 150

Answer: $150 interest paid

Total repayment: $1,000 + $150 = $1,150

Example 3: 6 Months

You invest $2,000 at 4% annual interest for 6 months. How much interest?

Given:

• P = $2,000
• R = 4% = 0.04
• T = 6 months = 0.5 years (6/12)

Calculate: I = 2,000 × 0.04 × 0.5 = 40

Answer: $40 interest

Finding Total Amount

Total Amount = Principal + Interest

A = P + I

Example: Find Total

Principal = $800, Interest rate = 6%, Time = 4 years

Step 1: Find interest

• I = 800 × 0.06 × 4 = 192

Step 2: Add to principal

• Total = 800 + 192 = $992

Answer: $992 total

Finding Principal

If you know I, R, and T, solve for P!

P = I / (RT)

Example: Find Principal

You want to earn $60 interest at 4% for 3 years. How much should you deposit?

Given:

• I = $60
• R = 0.04
• T = 3 years

Solve: P = 60 / (0.04 × 3) = 60 / 0.12 = 500

Answer: Deposit $500

Finding Rate

If you know I, P, and T, solve for R!

R = I / (PT)

Example: Find Rate

You invest $1,200 for 2 years and earn $96 interest. What's the rate?

Given:

• I = $96
• P = $1,200
• T = 2 years

Solve: R = 96 / (1,200 × 2) = 96 / 2,400 = 0.04

Convert to percent: 0.04 = 4%

Answer: 4% interest rate

Finding Time

If you know I, P, and R, solve for T!

T = I / (PR)

Example: Find Time

You invest $500 at 5% and earn $75 interest. How long?

Given:

• I = $75
• P = $500
• R = 0.05

Solve: T = 75 / (500 × 0.05) = 75 / 25 = 3

Answer: 3 years

Time in Months

Remember: Convert months to years by dividing by 12!

Examples:

• 6 months = 6/12 = 0.5 years
• 9 months = 9/12 = 0.75 years
• 18 months = 18/12 = 1.5 years

Example: 15 Months

Borrow $600 at 8% for 15 months. Find interest.

Convert time: 15/12 = 1.25 years

Calculate: I = 600 × 0.08 × 1.25 = 60

Answer: $60 interest

Simple vs. Compound Interest

Simple interest: Calculated only on principal

• Same interest amount each year
• I = PRT

Compound interest: Interest earns interest

• Interest amount grows each year
• More complex formula (covered in advanced courses)

Simple interest is easier to calculate!

Real-World Applications

Savings bonds: Government pays simple interest

• Invest $100 at 2% for 10 years

Car loans: Often use simple interest initially

• Borrow $15,000 at 6% for 5 years

Personal loans: Calculate total repayment

• Borrow $5,000 at 7% for 3 years

Investment planning: Estimate earnings

• How much will $10,000 grow in 5 years at 4%?

Comparison shopping: Compare loan offers

• Which rate saves more money?

Tips for Success

Always:

• Convert percent to decimal (5% → 0.05)
• Convert months to years (divide by 12)
• Label your answer with $ or %
• Check if answer makes sense

Common mistakes:

• Forgetting to convert percent to decimal
• Using months instead of years
• Confusing interest with total amount

Practice