worksheet on simple and compound interest

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22-11-2024

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Meta Description: Master the difference between simple and compound interest! This comprehensive worksheet guide includes practice problems, formulas, and explanations to boost your financial literacy. Learn to calculate interest and understand its impact on investments and loans. Perfect for students and anyone wanting to improve their financial skills.

Understanding Interest: Simple vs. Compound

Interest is the cost of borrowing money or the reward for lending it. There are two main types: simple and compound interest. Let's break them down.

Simple Interest

Simple interest is calculated only on the principal amount (the initial amount borrowed or invested). The formula is straightforward:

Simple Interest = Principal × Rate × Time

Where:

• Principal (P): The initial amount.
• Rate (R): The annual interest rate (expressed as a decimal).
• Time (T): The time period in years.

Example: You invest $1,000 at a 5% simple interest rate for 3 years.

Simple Interest = $1000 × 0.05 × 3 = $150

Your total amount after 3 years would be $1,000 + $150 = $1,150.

Compound Interest

Compound interest is calculated on the principal amount plus any accumulated interest. This means your interest earns interest, leading to faster growth. The formula is:

A = P (1 + r/n)^(nt)

Where:

• A: The future value of the investment/loan, including interest.
• P: The principal amount.
• r: The annual interest rate (decimal).
• n: The number of times that interest is compounded per year (e.g., 1 for annually, 4 for quarterly, 12 for monthly).
• t: The number of years.

Example: You invest $1,000 at a 5% interest rate compounded annually for 3 years.

A = $1000 (1 + 0.05/1)^(1*3) = $1157.63

Your total amount after 3 years would be approximately $1,157.63. Notice the difference compared to simple interest!

Worksheet: Simple and Compound Interest Problems

Here's a worksheet to test your understanding. Solve the following problems, showing your work.

Section 1: Simple Interest

1. Calculate the simple interest on a $5,000 loan at 8% interest for 2 years.
2. You deposit $2,000 in a savings account that earns 4% simple interest. How much will you have after 5 years?
3. If you earn $75 in simple interest on a $500 investment over 3 years, what was the annual interest rate?

Section 2: Compound Interest

4. Calculate the compound interest earned on a $10,000 investment at 6% interest compounded annually for 4 years.
5. You borrow $3,000 at 7% interest compounded monthly. What will you owe after 2 years?
6. An investment grows from $1,500 to $2,000 in 3 years with interest compounded annually. What is the approximate annual interest rate? (Hint: You might need to use a calculator or iterative methods to solve for 'r'.)

Section 3: Comparing Simple and Compound Interest

7. Compare the total amounts after 10 years for an initial investment of $1000 with a 5% simple interest rate vs. a 5% interest rate compounded annually. What’s the difference? Why?

8. Explain the difference between simple and compound interest in your own words. When is compound interest advantageous?

Solutions (Answers to Worksheet Problems)

(Note: Solutions are provided below to help you check your work. It's crucial to attempt the problems yourself first!)

Section 1:

1. Simple Interest = $5000 × 0.08 × 2 = $800
2. Total Amount = $2000 + ($2000 × 0.04 × 5) = $2400
3. Rate = (75 / (500 × 3)) = 0.05 or 5%

Section 2:

4. A = $10000 (1 + 0.06/1)^(1*4) ≈ $12624.77; Compound Interest ≈ $2624.77
5. A = $3000 (1 + 0.07/12)^(12*2) ≈ $3458.89
6. This requires iterative solution or a financial calculator. The approximate annual interest rate is around 10%.

Section 3:

7. Simple interest: $1000 + ($1000 * 0.05 * 10) = $1500. Compound Interest: $1000 (1 + 0.05)^10 ≈ $1628.89. Difference: $128.89. Compound interest grows faster because interest earned also earns interest.

8. Simple interest only applies to the original principal; compound interest applies to the principal and accumulated interest, leading to exponential growth. Compound interest is advantageous for long-term investments.

This worksheet provides a solid foundation in understanding and calculating simple and compound interest. Remember to practice regularly to solidify your grasp of these essential financial concepts.