Financial Mathematics · SS 3
Depreciation
Find the value of something that loses a fixed percentage of its value each year, like a car.
- V = P(1 − r100)n
What the letters mean
- V
- the value after n years
- P
- the original value
- r
- the rate of depreciation per cent per year
- n
- the number of years
Worked example
A machine bought for ₦800,000 depreciates by 20% a year. Find its value after 2 years.
Step 1: Put in the formula
V = 800,000 × (0.8)2
Step 2: Work it out
= 800,000 × 0.64 = ₦512,000
Final answer: ₦512,000
See it
Play with this picture from the Depreciation lesson.
Reducing balance (value now)Straight line: 20% of the original every year
Principal P₦2,000,000
Rate of loss r20%
Years n2
V = ₦2,000,000 × 0.82 = ₦1,280,000
Year 2: ₦1,600,000 − ₦320,000 (20% of last year's value, not of ₦2,000,000)
Total depreciation = ₦2,000,000 − ₦1,280,000 = ₦720,000 · straight line (20% of the original each year) would say ₦800,000
Multiplier 1 − 20/100 = 0.8 · amounts rounded to the nearest kobo