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Compound interest and depreciation are among the most practical topics in GCSE Mathematics — they apply directly to savings, loans, and the value of cars and other assets. AQA tests these topics on both Foundation and Higher tier papers. This lesson covers simple interest, compound interest using multipliers, and depreciation.
Simple interest is interest calculated only on the original amount (the principal). The interest is the same each year.
Simple Interest = (Principal x Rate x Time) / 100
Where:
Worked Example 1: 2,000 pounds is invested at 3% simple interest per year. How much interest is earned after 5 years?
Compound interest is interest calculated on the original amount plus any interest already earned. Each year, the interest is added to the total, and the next year's interest is calculated on this new, larger amount.
| Year | Simple Interest (3% on 1,000) | Compound Interest (3% on 1,000) |
|---|---|---|
| 0 | 1,000.00 | 1,000.00 |
| 1 | 1,030.00 | 1,030.00 |
| 2 | 1,060.00 | 1,060.90 |
| 3 | 1,090.00 | 1,092.73 |
| 4 | 1,120.00 | 1,125.51 |
| 5 | 1,150.00 | 1,159.27 |
Exam Tip: After year 1, simple and compound interest give the same result. The difference only appears from year 2 onwards. If a question asks about 1 year, both methods give the same answer.
The most efficient way to calculate compound interest is using a multiplier.
Final Amount = Principal x (Multiplier) to the power of n
Where:
| Interest Rate | Multiplier |
|---|---|
| 2% | 1.02 |
| 3% | 1.03 |
| 5% | 1.05 |
| 7.5% | 1.075 |
| 10% | 1.10 |
| 0.5% | 1.005 |
Worked Example 2: 5,000 pounds is invested at 4% compound interest per year for 3 years. Find the total amount.
Interest earned = 5,624.32 - 5,000 = 624.32 pounds
Worked Example 3: 8,000 pounds is invested at 2.5% compound interest for 6 years. Find the total amount.
graph TD
A[Compound Interest Calculation] --> B[Identify: Principal, Rate, Time]
B --> C[Calculate multiplier = 1 + rate/100]
C --> D[Final Amount = Principal x multiplier to the power n]
D --> E[Interest = Final Amount - Principal]
Exam Tip: On the calculator paper, use the power button to raise the multiplier to the power of n. Do NOT round the multiplier mid-calculation — only round the final answer.
Depreciation is the opposite of compound interest — the value of an asset decreases over time by a fixed percentage each year.
Final Value = Original Value x (Multiplier) to the power of n
Where:
| Depreciation Rate | Multiplier |
|---|---|
| 5% | 0.95 |
| 10% | 0.90 |
| 15% | 0.85 |
| 20% | 0.80 |
| 25% | 0.75 |
| 12.5% | 0.875 |
Worked Example 4: A car is bought for 15,000 pounds. It depreciates at 20% per year. What is its value after 3 years?
Worked Example 5: A computer is bought for 1,200 pounds and depreciates at 30% per year. What is it worth after 4 years?
Worked Example 6: 6,000 pounds is invested for 4 years. Compare the returns at 5% simple interest and 5% compound interest.
Simple Interest:
Compound Interest:
Difference = 7,293.04 - 7,200 = 93.04 pounds more with compound interest.
Exam Tip: Questions asking you to compare simple and compound interest are worth 4-5 marks. Show BOTH calculations clearly and state the difference.
Worked Example 7: A savings account pays 3% compound interest. If 4,000 pounds is invested, after how many years will it first exceed 4,500 pounds?
Use trial and improvement:
It first exceeds 4,500 after 4 years.
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