Compound Interest and Depreciation: GCSE Maths

What is the difference between simple and compound interest?

Simple interest adds the same fixed amount every year, calculated on the original sum. Compound interest adds interest on the total accumulated so far — principal plus all previous interest. This means the growth accelerates year on year.

By Year 4, compound interest has earned £64.10 more than simple interest on the same starting amount.

What is the multiplier method?

The multiplier is the decimal you multiply by to apply one percentage change:

• An increase of r%: multiplier = 1 + r/100
• A decrease of r%: multiplier = 1 − r/100

For compound interest of 5% per year: multiplier = 1.05. For depreciation of 8% per year: multiplier = 0.92.

Applying the same multiplier n times gives: Final = Start × multiplier^n

How do you calculate compound interest?

Worked example: £2000 is invested at 3% compound interest per year. How much is it worth after 4 years?

1. Rate = 3%, so multiplier = 1 + 3/100 = 1.03.
2. Number of years n = 4.
3. Final value = £2000 × 1.03⁴.
4. 1.03⁴ = 1.03 × 1.03 × 1.03 × 1.03 = 1.12550881.
5. Final value = £2000 × 1.12550881 = £2251.02 (to the nearest penny).

Check: Simple interest would give £2000 × 0.03 × 4 = £240 extra, i.e. £2240. Compound gives more (£2251.02), which makes sense.

How do you calculate depreciation?

Worked example: A car bought for £14 000 depreciates at 12% per year. What is it worth after 3 years?

1. Rate = 12% decrease, so multiplier = 1 − 12/100 = 0.88.
2. n = 3.
3. Value = £14 000 × 0.88³.
4. 0.88³ = 0.88 × 0.88 × 0.88 = 0.681472.
5. Value = £14 000 × 0.681472 = £9540.61 (to the nearest penny).

How do you find the original value using the reverse?

If the final value and multiplier are given, divide to reverse the process.

Example: After 2 years of 5% compound interest, an account holds £2205. What was the original deposit?

1. Multiplier = 1.05; n = 2; multiplier² = 1.1025.
2. Original = £2205 ÷ 1.1025 = £2000.

What exam mistakes should you avoid?

• Using simple interest instead of compound. Multiplying the interest rate by the number of years gives simple interest. Compound interest requires raising the multiplier to a power.
• Rounding intermediate steps. Keep the full calculator value until the final answer. Rounding 1.03⁴ to 1.126 early gives a wrong final figure.
• Getting the multiplier sign wrong. A 12% decrease uses 0.88, not 1.12. Double-check: if something is losing value, your multiplier must be less than 1.

Frequently asked questions

Why does compound interest grow faster than simple interest?

Because compound interest is calculated on an ever-increasing base. Each year the interest itself earns interest. Over long periods this "interest on interest" effect becomes very significant — the mathematical term for this growth is exponential.

Is depreciation the same calculation as compound interest?

Yes — the formula is identical. The only difference is that depreciation uses a multiplier less than 1 (e.g. 0.85), so the value decreases, while compound interest uses a multiplier greater than 1 (e.g. 1.05), so the value increases. Both involve repeated multiplication by the same factor.

What does the GCSE question mean by "to the nearest penny"?

Round your answer to 2 decimal places, since money is measured in pounds and pence. For example, £1256.784… rounds to £1256.78. If the digit in the third decimal place is 5 or more, round the second decimal place up.

How do you use a calculator efficiently for compound interest?

Type: starting value × (multiplier) ^ n and press equals. On most scientific calculators the ^ or x^y key raises a number to a power. For example: 2000 × 1.03 ^ 4 = 2251.018... Check that your answer is larger (interest) or smaller (depreciation) than the starting value — if not, you have used the wrong multiplier.

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