Functional Skills Level 2 — Compound Interest

Compound Interest

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Simple vs Compound Interest

Simple interest gives you the same amount of interest every year, always calculated on the original principal.

Compound interest adds the interest to your running total each year. The next year’s interest is calculated on the new (larger) total — so it grows faster and faster over time.

£1000 at 10% — Simple vs Compound Growth Simple Compound Year 1 Year 2 Year 3 £1100 £1100 £1200 £1210 £1300 £1331 The Snowball Effect — Compound Interest Grows Each Year Year 1 £1000 ×1.10 Year 2 £1100 on £1000 ×1.10 Year 3 £1210 on £1100 ×1.10 Year 4 £1331 on £1210
YearSimple InterestSimple TotalCompound InterestCompound Total
1£100£1100£100£1100
2£100£1200£110£1210
3£100£1300£121£1331
Notice that after just 3 years compound interest gives £31 more. Over longer periods the difference becomes very large indeed.

📄 Example 1 — Simple Interest: £1000 at 10% for 3 years

Formula
\(I = \dfrac{P \times r \times t}{100} = \dfrac{1000 \times 10 \times 3}{100} = £300\)
Total
Total = £1000 + £300 = £1300
Same £100 every year — always calculated on the original £1000

📄 Example 2 — Compound Interest: £1000 at 10% for 3 years

Year 1
£1000 × 1.10 = £1100
Year 2
£1100 × 1.10 = £1210  (interest now on £1100)
Year 3
£1210 × 1.10 = £1331  (interest now on £1210)
Each year’s interest is added to the total — making the following year’s interest larger
Quick Check 1 — Simple vs Compound Interest
Question 1 of 10
Calculating Compound Interest Year by Year

At FS2 level, you calculate compound interest by multiplying the running total by the multiplier once for each year. The multiplier for a rate of \(r\%\) is \(1 + \frac{r}{100}\).

For example, 5% growth gives a multiplier of 1.05. You multiply by 1.05 once for every year.

Multiplier = \(1 + \dfrac{r}{100}\)  —  multiply by this once per year
£1000 at 5% — Year-by-Year Multiplier Method Start £1000 ×1.05 Year 1 £1050 ×1.05 Year 2 £1102.50 ×1.05 Year 3 £1157.63 Each year the interest is added to the total and the next year's interest is larger
FS2 method: Work out the multiplier (e.g. 5% → 1.05), then multiply the running total by it once for each year. Write down each year’s total to keep track.

📄 Example 1 — £1000 at 5% compound interest for 3 years

Multiplier
5% growth → multiplier = \(1 + \frac{5}{100} = 1.05\)
Year 1
£1000 × 1.05 = £1050.00
Year 2
£1050 × 1.05 = £1102.50
Year 3
£1102.50 × 1.05 = £1157.63  (to 2 d.p.)
Each year the interest is on a bigger total — so the interest earned grows each year

📄 Example 2 — £2500 at 3% compound interest for 3 years

Multiplier
3% growth → multiplier = 1.03
Year 1
£2500 × 1.03 = £2575.00
Year 2
£2575 × 1.03 = £2652.25
Year 3
£2652.25 × 1.03 = £2731.82  (to 2 d.p.)
Quick Check 2 — Year-by-Year Compound Interest
Question 1 of 10
Compound Decrease — Depreciation

The same year-by-year method applies to things that lose value over time. This is called depreciation.

If something decreases by 15% per year, the multiplier is \(1 - \tfrac{15}{100} = 0.85\). You multiply the running value by 0.85 once for each year.

Multiplier for decrease = \(1 - \dfrac{r}{100}\)  —  multiply by this once per year
Car Depreciation at 15% Per Year — Year-by-Year Method New Car £8,000 ×0.85 After 1 yr £6,800 ×0.85 After 2 yrs £5,780 ×0.85 After 3 yrs £4,913 Each year the value is 85% of the previous year — the car loses over £3000 in 3 years

📄 Example 1 — Car: £8000 depreciating at 15% per year for 3 years

Multiplier
15% decrease → multiplier = \(1 - 0.15 = 0.85\)
Year 1
£8000 × 0.85 = £6800.00
Year 2
£6800 × 0.85 = £5780.00
Year 3
£5780 × 0.85 = £4913.00
The car has lost over £3000 — more than 38% of its original value in just 3 years

📄 Example 2 — TV worth £600 depreciates at 20% per year for 2 years

Multiplier
20% decrease → multiplier = \(1 - 0.20 = 0.80\)
Year 1
£600 × 0.80 = £480.00
Year 2
£480 × 0.80 = £384.00
Common mistake: A 20% decrease for 2 years does not mean a total 40% loss. After Year 1 you have £480 (not £360), and Year 2 takes 20% of £480 — the total loss is 36%, not 40%.
Quick Check 3 — Compound Decrease and Depreciation
Question 1 of 10

Practice: Compound Interest

Find the total amount after interest. Enter your answers as numbers.

#QuestionAnswerResult
1£1,000 invested at 10% compound interest for 2 years
2£2,000 invested at 5% compound interest for 2 years
3£1,500 invested at 20% compound interest for 1 year
4£4,000 invested at 10% compound interest for 1 year
5£1,000 invested at 10% compound interest for 3 years
6£2,500 invested at 4% compound interest for 2 years
7£5,000 invested at 8% compound interest for 2 years
8£3,000 invested at 10% compound interest for 3 years
9£1,200 invested at 15% compound interest for 1 year
10£600 invested at 20% compound interest for 2 years
11£1,000 invested at 5% compound interest for 2 years
12£500 invested at 10% compound interest for 3 years
13£2,000 invested at 4% compound interest for 2 years
14£800 invested, value falls by 15% (compound decrease) for 1 year. What is it worth?
15£1,500 invested at 8% compound interest for 2 years

⚠ Things to Watch Out For

  • Using simple interest instead of compound: With simple interest you always calculate interest on the original amount. With compound interest you must update the total each year and calculate the next year's interest on the new total.
  • Getting the multiplier wrong for a decrease: 15% depreciation per year means you multiply by 0.85 (not 1.15 and not 0.15). Decrease multiplier = 1 − (rate ÷ 100).
  • Getting the multiplier wrong for an increase: 5% growth per year means you multiply by 1.05 (not 0.05 and not 5). Increase multiplier = 1 + (rate ÷ 100).
  • Forgetting to update the total each year: Each year you must multiply the previous year's total — not the original amount — by the multiplier. Write down each year's running total to avoid this.
  • Giving total interest instead of total amount: If the question asks for the interest earned, you must subtract the original principal from your final total: Interest = Final total − Starting amount.
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