Compound Interest: A Comprehensive Guide for GCSE Mathematics
Introduction
Compound interest is the growth of money over time at a specific interest rate, compounded periodically. It plays a crucial role in many financial scenarios, including savings, loans, and investments. Understanding compound interest empowers students to make informed decisions about their finances.
Key Concepts and Definitions
- Principal: The initial amount invested or borrowed.
- Interest Rate: The percentage rate at which interest is charged or earned.
- Compounding Period: The frequency at which interest is added to the account.
- Future Value: The total amount of money in the account after a certain period of time.
Step-by-Step Calculations
- Formula: Future Value = Principal x (1 + Interest Rate/Compounding Period)^(Number of Compounding Periods)
- Example: If you deposit £100 for 5 years at an annual interest rate of 5% compounded annually, your future value would be:
- FV = £100 x (1 + 0.05/1)^5 = £127.63
Common Mistakes to Avoid
- Assuming simple interest instead of compound interest.
- Mixing up the compounding period and interest rate.
- Forgetting to include the principal in the final calculation.
Practice Problems
- Question: Find the future value of £500 invested for 10 years at an interest rate of 3% compounded quarterly.
- Future Value = £500 x (1 + 0.03/4)^(40) = £662.08
Conclusion
Compound interest is an essential concept in GCSE Mathematics and beyond. By understanding its principles, you can make smarter financial decisions.
Tips for Exam Success
- Practice using the formula and solving problems.
- Pay attention to the compounding period and interest rate.
- Check your calculations carefully.
FAQs
- What is the difference between simple and compound interest?
Simple interest calculates interest based on the principal, while compound interest calculates interest based on the growing balance.
- How does the compounding period affect the future value?
A shorter compounding period leads to a higher future value as interest is added more frequently.