Find the multiplier
A savings account grows by 5% each year. Find the multiplier.
For growth, add the rate as a decimal to 1.
Year 8
Compound interest and depreciation
Use the percentage multiplier method to calculate compound interest and depreciation over several years, and explain why compound growth is not the same as simple growth.
Lesson overview
Number - percentage multiplier method
A percentage multiplier increases an amount by r% when you multiply by (1 + r/100), or decreases it by r% when you multiply by (1 - r/100). Compound interest means each year's interest is calculated on the new total, not the original amount -- so the amount grows faster each year. Depreciation works the same way in reverse: an item such as a car loses the same percentage of its current value each year, so the amount lost gets smaller over time.
Repeat the multiplier for each year
£200 grows at 10% compound interest for 3 years.
| Year 0 | Year 1 | Year 2 | Year 3 |
|---|---|---|---|
| 200 | 220 | 242 | 266.20 |
Each year, multiply the previous total by 1.10 -- not the original 200.
Depreciation uses the same method in reverse
A car worth £8000 depreciates by 15% each year.
For a decrease, subtract the rate as a decimal from 1.
Worked example
£500 is invested at 4% compound interest per year. Find the value after 3 years.
| Year 1 | Year 2 | Year 3 |
|---|---|---|
| 520.00 | 540.80 | 562.43 |
- Find the multiplier: 1 + 0.04 = 1.04.
- Year 1: 500 × 1.04 = 520.
- Year 2: 520 × 1.04 = 540.80.
- Year 3: 540.80 × 1.04 = 562.43 (to the nearest penny). This is the same as 500 × .
Try it
Find the multiplier first, then decide whether to repeat it year by year or raise it to a power.
Question 1
A value grows by 8% each year. What is the multiplier?
Question 2
A value depreciates by 20% each year. What is the multiplier?
Question 3
£300 is invested at 10% compound interest for 2 years. What is the value after 2 years?
| Year 1 | Year 2 |
|---|---|
| 330 | 363 |
Question 4
Why is compound interest usually more than simple interest over the same time?
Question 5
A car worth £12000 depreciates by 10% per year. What is it worth after 2 years?
| Year 1 | Year 2 |
|---|---|
| 10800 | 9720 |
Common mistakes
Watch for these when working through the lesson.
- Using the same multiplier method as simple interest -- applying the percentage to the original amount every year instead of the running total.
- Using a multiplier greater than 1 for a decrease, or less than 1 for an increase.
- Forgetting that the power in (multiplier)^n must match the number of years.
Related topics
These ideas fit closely with this lesson.
- Percentages of amounts without a calculator.
- Simple interest, compound interest comparison and financial maths.
- Rounding to significant figures.