Numerical aptitude · Percentages and money
Compound interest, made easy
💡 The idea
With compound interest, each year’s interest is added to the money, so next year you earn interest on the interest too.
$1,000→+10% → $1,100→+10% → $1,210
🧭 The method: 3 steps
- Year 1: add the interest to get a new total.
- Year 2: work out the interest on the new total and add it.
- Keep going for each year. Interest = final amount − the money at the start.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. Compound interest on $1,000 at 10% for 2 years?
- Year 1: 10% of 1,000 = 100 → 1,100
- Year 2: 10% of 1,100 = 110 → 1,210
- Interest = 1,210 − 1,000 = $210
⚡ Shortcut: 1000 × 1.1 × 1.1 = 1210.
Example 2. Difference between compound and simple interest on $5,000 for 2 years at 10%?
- Simple: 500 + 500 = 1,000
- Compound: 500 + 550 = 1,050
- Difference = $50
⚡ Shortcut: P × (R/100)² = 5000 × 0.01 = 50.
Example 3. $8,000 at 10% a year, added every 6 months, for 1 year?
- Half-yearly: 5% each time, 2 times
- 8,000 × 1.05 = 8,400
- 8,400 × 1.05 = $8,820
⚠️ Where people go wrong
- Don’t use simple interest by mistake: it misses the interest on interest.
- Half-yearly means half the rate, twice as often.
- Read whether they want the interest or the amount.
📌 Remember
- Amount = P × (1 + R/100)^years
- CI − SI for 2 years = P × (R/100)²
- 10% for 3 years: × 1.331