GCSE Maths Number - How to Solve: Simple and Compound Interest

How to Solve: Simple and Compound Interest

Complete Guide (GCSE / A-Level Physics, Chemistry, Biology – Financial Maths Applications)

Introduction

"Mastering simple and compound interest doesn’t just help you pass your maths exam—it lets you calculate how much your £1,000 savings will grow to in 5 years, or how much debt you’ll owe on a student loan. This topic appears in GCSE Maths (Foundation & Higher), A-Level Maths (Pure), and even A-Level Physics (financial modelling). Get it right, and you’ll bank 5-10 marks in your exam—easily."

WHAT YOU NEED TO KNOW FIRST

Before starting, you must understand: 1. Percentage calculations – How to find 5% of £200. 2. Rearranging formulas – Solving for P, r, or t when given the others. 3. Units consistency – Ensuring time (t) is in years (not months) unless specified.

KEY TERMS & FORMULAS

Key Terms

Formulas

1. Simple Interest

Formula: [ I = P \times r \times t ] Variables: - ( I ) = Interest earned/paid (£) - ( P ) = Principal (£) - ( r ) = Annual interest rate (as a decimal, e.g., 5% = 0.05) - ( t ) = Time in years

MEMORISE THIS – Not always given on exam sheets.

Total Amount (A): [ A = P + I = P(1 + rt) ]

2. Compound Interest

Formula: [ A = P \left(1 + \frac{r}{n}\right)^{nt} ] Variables: - ( A ) = Total amount after time t (£) - ( P ) = Principal (£) - ( r ) = Annual interest rate (decimal) - ( n ) = Number of times interest is compounded per year (e.g., n=12 for monthly) - ( t ) = Time in years

MEMORISE THIS – Often given, but know how to use it.

If compounded annually (n=1): [ A = P(1 + r)^t ]

Interest Earned (I): [ I = A - P ]

STEP-BY-STEP METHOD

For Simple Interest Problems

Step 1: Identify the principal (P), rate (r), and time (t). - Convert % to decimal (e.g., 4% → 0.04). - Convert time to years (e.g., 6 months = 0.5 years).

Step 2: Plug into the formula: [ I = P \times r \times t ]

Step 3: Calculate the total amount (A) if needed: [ A = P + I ]

Step 4: Round to 2 decimal places (for money).

For Compound Interest Problems

Step 1: Identify P, r, n, and t. - Convert % to decimal. - Ensure t is in years. - n = 1 (annually), 2 (semi-annually), 4 (quarterly), 12 (monthly).

Step 2: Plug into the formula: [ A = P \left(1 + \frac{r}{n}\right)^{nt} ]

Step 3: Calculate interest earned (I) if needed: [ I = A - P ]

Step 4: Round to 2 decimal places.

WORKED EXAMPLES

Example 1 – Basic Simple Interest

Question: £800 is invested at 3% simple interest per year for 4 years. Calculate the interest earned.

Step 1: Identify variables. - ( P = £800 ) - ( r = 3\% = 0.03 ) - ( t = 4 ) years

Step 2: Plug into formula. [ I = 800 \times 0.03 \times 4 ]

Step 3: Calculate. [ I = 800 \times 0.12 = £96 ]

Answer: £96

What we did and why: - Converted % to decimal (0.03). - Multiplied principal × rate × time. - No rounding needed (exact answer).

Example 2 – Medium Compound Interest

Question: £1,200 is invested at 5% compound interest, compounded annually for 3 years. Calculate the total amount.

Step 1: Identify variables. - ( P = £1,200 ) - ( r = 5\% = 0.05 ) - ( n = 1 ) (annually) - ( t = 3 ) years

Step 2: Plug into formula. [ A = 1200 \left(1 + \frac{0.05}{1}\right)^{1 \times 3} ] [ A = 1200 (1.05)^3 ]

Step 3: Calculate. [ 1.05^3 = 1.157625 ] [ A = 1200 \times 1.157625 = £1,389.15 ]

Answer: £1,389.15

What we did and why: - Used the annual compounding formula (n=1). - Calculated the power first (1.05³). - Multiplied by principal and rounded to 2 d.p.

Example 3 – Exam-Style (Disguised)

Question: A student borrows £600 at 8% simple interest per year. After 18 months, how much do they owe in total?

Step 1: Identify variables. - ( P = £600 ) - ( r = 8\% = 0.08 ) - ( t = 18 ) months = 1.5 years

Step 2: Plug into formula. [ I = 600 \times 0.08 \times 1.5 ]

Step 3: Calculate. [ I = 600 \times 0.12 = £72 ]

Step 4: Total amount. [ A = P + I = 600 + 72 = £672 ]

Answer: £672

What we did and why: - Converted 18 months to 1.5 years (critical step!). - Used simple interest formula. - Added interest to principal for total amount.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP

"Right, listen up—this is your last-minute cheat sheet for simple and compound interest.

Simple Interest: - Formula: ( I = P \times r \times t ). - Convert % to decimal (5% = 0.05). - Time must be in years (6 months = 0.5 years). - Total amount = ( P + I ).

Compound Interest: - Formula: ( A = P(1 + r/n)^{nt} ). - n = 1 (annual), 4 (quarterly), 12 (monthly). - Interest = ( A - P ).

Watch out for: - Time in months (convert to years!). - Compounding frequency (annual? monthly?). - Rounding (2 decimal places for money).

Exam tip: If the question says "simple interest", use ( I = Prt ). If it says "compounded", use the power formula. Double-check units—examiners love tricking you here!

Now go smash those 10 marks!"