EDEXCEL GCSE HIGHER MATHS - What is Compound and Simple Interest

Edexcel GCSE Higher Maths: Compound and Simple Interest

What is Interest?

Interest is an amount of money paid to you for lending money to someone else (like a bank) or earned by your savings account. It's a percentage of the original amount, called the principal.

Simple Interest

• Calculation: Interest is calculated only on the original principal amount.
• Formula: Simple Interest = (Principal x Rate x Time) / 100
• Where:
  • Principal (P): The initial amount of money borrowed or invested.
  • Rate (R): The percentage at which interest is calculated per year.
  • Time (T): The duration of the loan or investment in years.

Example:

You invest £500 at a simple interest rate of 5% per year for 3 years.

• Simple Interest = (500 x 5 x 3) / 100 = £75
• Total Amount = Principal + Simple Interest = £500 + £75 = £575

Compound Interest

• Calculation: Interest is calculated on the principal amount plus any accumulated interest from previous periods.
• Formula: Compound Interest = Principal (1 + Rate/100)^Time - Principal
• Where:
  • Principal (P): The initial amount of money borrowed or invested.
  • Rate (R): The percentage at which interest is calculated per year.
  • Time (T): The duration of the loan or investment in years.

Example:

You invest £500 at a compound interest rate of 5% per year for 3 years.

• Year 1: Interest = (500 x 5) / 100 = £25; Total Amount = £500 + £25 = £525
• Year 2: Interest = (525 x 5) / 100 = £26.25; Total Amount = £525 + £26.25 = £551.25
• Year 3: Interest = (551.25 x 5) / 100 = £27.56; Total Amount = £551.25 + £27.56 = £578.81

Or using the formula:

• Compound Interest = 500 (1 + 5/100)^3 - 500 = £78.81
• Total Amount = Principal + Compound Interest = £500 + £78.81 = £578.81

Key Differences:

• Simple interest is a fixed amount calculated only on the principal.
• Compound interest is calculated on the principal plus any accumulated interest, leading to exponential growth over time.

Which is Better?

Compound interest is generally more beneficial for investors as it generates higher returns over time. However, the type of interest that applies will be clearly stated in loan or investment agreements.