Study guides › Level 6 · Master

Growth that builds on itself (compound growth)

Level 6 · Master · for questions like “$1,000 grows 10% every year. How much after 3 years?”

💡 The idea

Each year the growth is worked out on the new amount, so it grows faster and faster.

After n years: start × (1 + rate)ⁿ

🪜 The steps

1. Turn the percent into a multiplier: 10% growth means × 1.10.
2. Multiply year by year, or once by the multiplier to the power n.

✏️ Worked examples

1. $1,000 at 10% for 3 years: 1,000 → 1,100 → 1,210 → $1,331.

2. $500 at 20% for 2 years: 500 → 600 → $720.

⚠️ Watch out

• Not the same as 10% of the start each year. That gives $1,300, not $1,331.
• Round money at the end, not at every step.

🎯 Try these

1. $2,000 at 10% for 2 years
2. $800 at 50% for 2 years
3. $1,000 at 20% for 3 years

Answers: 1) $2,420 2) $1,800 3) $1,728

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.