Understanding Compound Interest and Percentage Increases in GCSE Mathematics
When tackling GCSE Maths higher tier calculator paper practice, compound interest calculations represent a crucial topic that frequently appears in examinations. This comprehensive explanation breaks down a complex financial mathematics problem involving multi-year investments and percentage increases.
In financial mathematics, compound interest builds upon previous interest earned, creating exponential growth over time. Consider an investment of £2000 with varying interest rates over three years. The first year applies a 2.5% rate, followed by two years at rate x%, resulting in a final amount of £2124.46. To solve for the unknown rate, we must understand how compound interest accumulates year by year.
Definition: Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. The formula is A = P1+rⁿ, where A is the final amount, P is the principal, r is the interest rate asadecimal, and n is the number of years.
The practical application extends beyond just savings accounts. In the second part of this exploration, we examine percentage increases in real-world contexts, specifically looking at train ticket price increases. When a weekly ticket increases by 12.5% to reach £225, we must work backwards to find the original price, demonstrating the reverse calculation of percentage changes.