Depreciation: The Value Drop
Use A = P(1 - r/100)^n to find the value of an item after it loses value.
Equation
y = 50000*(1-5/100)^x
Graph
Table
| x | y |
|---|---|
| 0 | 50000 |
| 1 | 47500 |
| 2 | 45125 |
| 3 | 42868.75 |
| 4 | 40725.31 |
What this lesson covers
What you do
You shape the function y = 50000*(1-p/100)^x and watch the graph answer.
Challenges to clear
- Set the depreciation rate p to 10%. Then look at the table: at x = 2 years the value is 40500.
- Year 1 shows 45000 — each year takes 10% of the CURRENT value, not the original.
- A different machine, bought for 40000. Slide V there first.
- Now the rate: after 2 years it is worth 25600. Each year strips a fifth off the CURRENT value, not the original.
Check yourself
If a car costs Rs 1,00,000 and depreciates at 20% per year, what is the correct expression for its value after 1 year?
Why do we use (1 - r/100) for depreciation instead of just subtracting r/100 at the end?
- 100000 * (1 - 20/100) — correct
- 100000 * (1 + 20/100)
- 100000 * (20/100)
- 100000 - 20
- Because depreciation applies to the remaining value each year, compounding the loss. — correct
- Because the formula is only for interest, not depreciation.
- Because subtracting at the end would give a higher value.
- Because we need to square the rate first.
Think about it
- A machine worth 50000 loses 10% each year. After year 1 it is worth 45000. And after year 2?