Simple Interest

When you borrow money or invest money, interest is the cost of borrowing or the reward for saving. Simple interest is a straightforward way to calculate interest based on the principal, rate, and time.

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What Is Simple Interest?

Simple interest is interest calculated only on the principal (original) amount.

Key Terms:

• Principal (P): The original amount of money borrowed or invested
• Rate (r): The percent of interest charged per year (as a decimal)
• Time (t): The length of time in years
• Interest (I): The amount charged or earned
• Total Amount (A): Principal + Interest

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The Simple Interest Formula

Formula: I = Prt

Where:

• I = Interest earned or paid
• P = Principal (starting amount)
• r = Rate (as a decimal, so 5% = 0.05)
• t = Time (in years)

Total Amount Formula: A = P + I or A = P(1 + rt)

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Calculating Simple Interest

Example 1: Basic Interest Calculation

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

Given:

• P = $500
• r = 4% = 0.04
• t = 3 years

Solution: I = Prt I = 500 × 0.04 × 3 I = 500 × 0.12 I = $60

Answer: You earn $60 in interest

Total amount: A = P + I = $500 +$60 = $560

Example 2: Interest Over Time

Maria borrows $1,200 at 6% simple interest for 2 years. How much interest will she owe?

Given:

• P = $1,200
• r = 6% = 0.06
• t = 2 years

Solution: I = Prt I = 1,200 × 0.06 × 2 I = 1,200 × 0.12 I = $144

Answer: She owes $144 in interest

Total to repay: A = $1,200 +$144 = $1,344

Example 3: Short-Term Interest

A credit card charges 18% annual interest. If you have a $300 balance for 6 months, how much interest accrues?

Given:

• P = $300
• r = 18% = 0.18
• t = 6 months = 0.5 years (important!)

Solution: I = Prt I = 300 × 0.18 × 0.5 I = 300 × 0.09 I = $27

Answer: $27 in interest for 6 months

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Converting Time to Years

Important: Time must be in YEARS for the formula I = Prt!

Common Conversions:

Months to Years:

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

Days to Years:

• 90 days = 90/365 years
• 180 days = 180/365 years
• Formula: days ÷ 365 = years

Example: Converting Time

You invest $800 at 5% for 9 months. Find the interest.

Step 1: Convert time to years

• 9 months = 9/12 = 0.75 years

Step 2: Calculate interest I = Prt I = 800 × 0.05 × 0.75 I = $30

Answer: $30 interest

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Finding Total Amount

Once you have the interest, add it to the principal!

Example: Investment Growth

You invest $2,000 at 3% for 4 years. What's the total amount after 4 years?

Step 1: Find interest I = Prt I = 2,000 × 0.03 × 4 I = $240

Step 2: Add to principal A = P + I A = $2,000 +$240 A = $2,240

Answer: Total amount is $2,240

Alternate method: A = P(1 + rt) A = 2,000(1 + 0.03 × 4) A = 2,000(1 + 0.12) A = 2,000 × 1.12 A = $2,240 ✓

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Solving for Different Variables

Sometimes you need to find P, r, or t instead of I!

Finding Principal (P)

Rearranged formula: P = I / (rt)

Example: How much should you invest at 5% for 2 years to earn $200 interest?

Given:

• I = $200
• r = 0.05
• t = 2

Solution: P = I / (rt) P = 200 / (0.05 × 2) P = 200 / 0.10 P = $2,000

Answer: Invest $2,000

Check: I = 2,000 × 0.05 × 2 = $200 ✓

Finding Rate (r)

Rearranged formula: r = I / (Pt)

Example: You invest $1,500 for 3 years and earn$180. What was the interest rate?

Given:

• I = $180
• P = $1,500
• t = 3

Solution: r = I / (Pt) r = 180 / (1,500 × 3) r = 180 / 4,500 r = 0.04 r = 4%

Answer: 4% interest rate

Check: I = 1,500 × 0.04 × 3 = $180 ✓

Finding Time (t)

Rearranged formula: t = I / (Pr)

Example: How long will it take to earn $150 interest on$1,000 at 5%?

Given:

• I = $150
• P = $1,000
• r = 0.05

Solution: t = I / (Pr) t = 150 / (1,000 × 0.05) t = 150 / 50 t = 3 years

Answer: 3 years

Check: I = 1,000 × 0.05 × 3 = $150 ✓

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Real-World Applications

Savings Accounts

Problem: You deposit $3,500 in a savings account with 2.5% simple interest. How much will you have after 5 years?

Solution: I = Prt = 3,500 × 0.025 × 5 = $437.50 A = P + I =$3,500 + $437.50 =$3,937.50

Answer: $3,937.50 total

Car Loans

Problem: A $15,000 car loan at 7% simple interest for 4 years. How much interest will you pay?

Solution: I = Prt = 15,000 × 0.07 × 4 = $4,200

Answer: $4,200 interest** **Total to repay:$15,000 + $4,200 =$19,200

Short-Term Loans

Problem: You borrow $800 for 3 months at 12% annual rate. How much interest?

Solution:

• Convert time: 3 months = 3/12 = 0.25 years
• I = Prt = 800 × 0.12 × 0.25 = $24

Answer: $24 interest

Comparing Investments

Problem: Which earns more interest?

• Option A: $2,000 at 4% for 3 years
• Option B: $1,500 at 6% for 3 years

Solution: Option A: I = 2,000 × 0.04 × 3 = $240 Option B: I = 1,500 × 0.06 × 3 =$270

Answer: Option B earns more ($270 vs$240)

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Simple Interest vs. Compound Interest

Simple Interest:

• Calculated only on the principal
• Interest does NOT earn interest
• Formula: I = Prt
• Grows linearly (same amount each year)

Compound Interest: (You'll learn this later!)

• Calculated on principal PLUS accumulated interest
• Interest earns interest
• Grows exponentially (faster over time)

Example Comparison:

$1,000 at 10% for 3 years:

Simple Interest:

• Year 1: $1,000 × 0.10 =$100 interest → Total: $1,100
• Year 2: $1,000 × 0.10 =$100 interest → Total: $1,200
• Year 3: $1,000 × 0.10 =$100 interest → Total: $1,300

Compound Interest:

• Year 1: $1,000 × 0.10 =$100 interest → Total: $1,100
• Year 2: $1,100 × 0.10 =$110 interest → Total: $1,210
• Year 3: $1,210 × 0.10 =$121 interest → Total: $1,331

Compound interest earns $31 more because interest earns interest!

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Using Tables to Track Interest

You can make a table to see how simple interest grows:

Example: $500 at 8% simple interest

| Year | Principal | Interest (I = Prt) | Total | |------|-----------|-------------------|-------| | 0 | $500 |$0 | $500 | | 1 |$500 | $40 |$540 | | 2 | $500 |$80 | $580 | | 3 |$500 | $120 |$620 | | 4 | $500 |$160 | $660 |

Notice: Interest increases by $40 each year (linear growth)

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Common Mistakes to Avoid

❌ Mistake 1: Forgetting to convert percent to decimal

• Wrong: I = 1,000 × 5 × 2 = $10,000
• Right: I = 1,000 × 0.05 × 2 = $100

❌ Mistake 2: Not converting time to years

• Wrong: I = 500 × 0.06 × 6 months = $180
• Right: I = 500 × 0.06 × 0.5 = $15

❌ Mistake 3: Using interest instead of total amount

• If asked for total, remember: A = P + I

❌ Mistake 4: Wrong formula rearrangement

• To find r: r = I/(Pt), not r = Pt/I

❌ Mistake 5: Confusing simple with compound interest

• Simple: Interest stays the same each period
• Compound: Interest grows each period

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Practice Strategy

Step 1: Identify what you're finding

• Interest (I)?
• Total amount (A)?
• Principal (P)?
• Rate (r)?
• Time (t)?

Step 2: List what you know

• Write down P, r, t, I, or A

Step 3: Convert if needed

• Rate: Convert percent to decimal (5% → 0.05)
• Time: Convert months/days to years

Step 4: Choose the right formula

• Finding I: I = Prt
• Finding A: A = P + I or A = P(1 + rt)
• Finding P: P = I/(rt)
• Finding r: r = I/(Pt)
• Finding t: t = I/(Pr)

Step 5: Solve and check

• Calculate carefully
• Plug answer back in to verify

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Memory Tricks

"I Put Rabbits Together" → I = P × r × t

Rate conversion:

• 5% = 0.05 (move decimal 2 places left)
• 12.5% = 0.125

Time conversion:

• Months: Divide by 12
• Days: Divide by 365

Check reasonableness:

• Interest should be less than principal (unless very long time!)
• Higher rate = more interest
• Longer time = more interest

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Quick Reference

Main Formula: I = Prt

Derived Formulas:

• A = P + I
• A = P(1 + rt)
• P = I/(rt)
• r = I/(Pt)
• t = I/(Pr)

Conversions:

• Percent to decimal: Divide by 100
• Months to years: Divide by 12
• Days to years: Divide by 365

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Summary

Simple interest is calculated using I = Prt where:

• P = Principal (original amount)
• r = Rate (as decimal)
• t = Time (in years)

Key Points:

• Interest is calculated only on the principal
• Convert rate to decimal (5% = 0.05)
• Convert time to years
• Total amount = Principal + Interest
• Can solve for any variable if you know the others

Applications:

• Savings accounts
• Loans
• Bonds
• Short-term investments

Understanding simple interest helps you make smart financial decisions about saving and borrowing money!