How to Solve: Simple Interest

How to Solve: Simple Interest

A Complete Guide for Students & Teachers

Introduction

"Imagine you lend $500 to a friend, and they pay you back $550 in a year. How much did they pay you for borrowing your money? That’s simple interest—and it’s on your exam!

What You Need To Know First

Before tackling simple interest, you must understand: 1. Percentage calculations – How to find 5% of 200. 2. Basic algebra – Solving for an unknown variable (e.g., P = I ÷ (r × t)). 3. Time units – Converting months to years (e.g., 6 months = 0.5 years).

Key Vocabulary

Formulas To Know

1. Simple Interest Formula

Formula: I = P × r × t

• I = Interest earned/paid (in dollars)
• P = Principal (starting amount)
• r = Annual interest rate (as a decimal, e.g., 5% = 0.05)
• t = Time in years (convert months to years: 6 months = 0.5 years)

✅ MEMORISE THIS – It’s the most important formula for simple interest.

2. Total Amount Formula

Formula: A = P + I or A = P(1 + r × t)

• A = Total amount after interest
• P, r, t = Same as above

✅ MEMORISE THIS – Useful for "total repayment" questions.

3. Solving for Principal (P)

Formula: P = I ÷ (r × t)

• Rearranged from I = P × r × t.

✅ Given on exam sheet (but memorising saves time).

4. Solving for Rate (r)

Formula: r = I ÷ (P × t)

✅ Given on exam sheet (but know how to use it).

5. Solving for Time (t)

Formula: t = I ÷ (P × r)

✅ Given on exam sheet (but practice converting years to months if needed).

Step-by-Step Method

How to Solve ANY Simple Interest Problem

Follow these steps in order for every question.

1. Read the question carefully. Underline:
2. The principal (P) (starting amount).
3. The interest rate (r) (convert % to decimal).
4. The time (t) (convert to years if needed).

5. What you’re asked to find (I, A, P, r, or t).

6. Write down the formula that matches what you need to find.

7. Need interest (I)? → I = P × r × t
8. Need total amount (A)? → A = P + I or A = P(1 + r × t)

9. Need principal (P), rate (r), or time (t)? → Rearrange I = P × r × t.

10. Convert units if needed.

11. Rate (r): Change % to decimal (e.g., 6% → 0.06).

12. Time (t): Convert months to years (e.g., 9 months = 9/12 = 0.75 years).

13. Plug numbers into the formula. Double-check:

14. Is r a decimal? (Not 5, but 0.05.)

15. Is t in years? (Not 6 months, but 0.5 years.)

16. Calculate and write the answer with units.

17. Money answers: $ (e.g., I = $30).
18. Rate answers: % (e.g., r = 4%).

19. Time answers: years or months (e.g., t = 2 years).

20. Check if the answer makes sense.

21. Interest should be less than the principal (unless t or r is very large).
22. Total amount (A) should be more than the principal (P).

Worked Example Using the Steps

Question: Sarah invests $800 at a simple interest rate of 3% per year. How much interest will she earn after 4 years?

Step-by-Step Solution:

1. Read & underline:
2. P = $800
3. r = 3% per year
4. t = 4 years

5. Find: I (interest)

6. Formula needed:
   I = P × r × t

7. Convert units:

8. r = 3% = 0.03

9. t = 4 years (already in years)

10. Plug in numbers:
    I = 800 × 0.03 × 4

11. Calculate:
    I = 800 × 0.12 = $96

12. Check:

13. $96 is less than $800 → Makes sense!

Answer: Sarah earns $96 in interest.

Worked Examples

Example 1 – Basic (Finding Interest)

Question: A bank offers 5% simple interest per year. If you deposit $1,200, how much interest will you earn in 3 years?

Solution: 1. P = $1,200, r = 5% = 0.05, t = 3 years 2. I = P × r × t 3. I = 1,200 × 0.05 × 3 4. I = 1,200 × 0.15 = $180

Answer: $180 in interest.

What we did and why: - We used I = P × r × t because we needed interest. - Converted 5% to 0.05 to match the formula. - Multiplied all three values to get the total interest.

Example 2 – Medium (Finding Total Amount)

Question: James borrows $500 at 4% simple interest per year. If he repays the loan after 18 months, what is the total amount he must pay back?

Solution: 1. P = $500, r = 4% = 0.04, t = 18 months = 1.5 years 2. A = P(1 + r × t) 3. A = 500(1 + 0.04 × 1.5) 4. A = 500(1 + 0.06) 5. A = 500 × 1.06 = $530

Answer: $530 total repayment.

What we did and why: - Used A = P(1 + r × t) because we needed the total amount. - Converted 18 months to 1.5 years (18 ÷ 12). - Calculated r × t first, then added 1, and finally multiplied by P.

Example 3 – Exam Style (Finding Rate)

Question: Liam earned $120 in simple interest after investing $1,500 for 2 years. What was the annual interest rate?

Solution: 1. I = $120, P = $1,500, t = 2 years 2. r = I ÷ (P × t) 3. r = 120 ÷ (1,500 × 2) 4. r = 120 ÷ 3,000 = 0.04 5. r = 0.04 = 4%

Answer: 4% per year.

What we did and why: - Used r = I ÷ (P × t) because we needed the rate. - Divided interest by (P × t) to isolate r. - Converted 0.04 to 4% for the final answer.

Common Mistakes

Exam Traps

1-Minute Recap

"Okay, let’s lock this in—simple interest in 60 seconds!

First, the formula: I = P × r × t. That’s Interest = Principal × Rate × Time. Memorise it!

Always convert: - Rate from % to decimal (5% → 0.05). - Time from months to years (6 months → 0.5 years).

If you need the total amount, use A = P + I or A = P(1 + r × t).

For exam questions: 1. Underline what’s given (P, r, t) and what’s asked (I, A, P, r, t). 2. Pick the right formula—don’t mix them up! 3. Plug in numbers carefully—double-check decimals and units. 4. Write the answer with $ or %—examiners take off marks for missing units!

Common traps? Time in months, rate as a decimal, and mixing up interest vs. total amount. Slow down, convert units, and you’ll nail it!

Now go practice—you’ve got this!

Final Tip for Teachers:

• Demo with real money: Show a $100 bill and calculate interest for 1 year at 5% ($5 interest).
• Use a timer: Give students 2 minutes to solve an exam-style question under pressure.
• Peer check: Have students swap papers and mark each other’s work using the step-by-step method.

Good luck—you’re now ready to ace simple interest! ?