Year 9: Financial mathematics - Identify the best deal

This cheat sheet helps you determine the best deal when comparing prices and offers.

Key Concepts

• Simple Interest: Interest earned on a sum of money over a set period. Formula: Interest = Principal x Rate x Time (where Rate is usually expressed as a decimal).
• Compound Interest: Interest earned on both the original amount (principal) and the accumulated interest. Formula: Future Value = Principal x (1 + Rate/Frequency) ^ Number of Periods (Frequency is how many times interest is compounded per year).
• Percentage Discount: A reduction in the original price, expressed as a percentage. Discount Amount = Original Price x Discount Percentage.
• Percentage Increase: The percentage by which something has increased in value. Percentage Increase = ((New Value - Old Value) / Old Value) x 100

Comparing Deals

1. Calculate the Total Cost: For each option, calculate the total cost including any interest or discounts.
2. Compare the Total Costs: The option with the lowest total cost is the best deal.
3. Consider the Time Period: A slightly higher interest rate might be worth it if you can keep the money invested for a longer time (especially with compound interest).
4. Don't just look at the headline price: Always calculate the total cost.

Example

Option A: $1000 at 5% simple interest for 3 years. Total Cost: $1000 + ($1000 x 0.05 x 3) = $1150

Option B: $1000 at 7% compound interest per year for 3 years. Future Value: $1000 * (1 + 0.07)^3 = $1202.70