Solved Real-World-Problem
to find the Value of an Asset after some time
if its
Current Value and
Percentage Decrease
is known
QUESTION: A certain forest covers an area of 2900 km². Suppose that each year this area decreases by 5%. What will the area be after 12 years?
SOLUTION:
FIRST METHOD:
Currently area of forest = 2900km²
After 1 year area of forest = 2900 – (0.05 × 2900)
= 2900 – 145
= 2755 km²
After 2 years area of forest = 2755 – (0.05 × 2755)
= 2755 – 138
= 2617 km²
After 3 years area of forest = 2617 – (0.05 × 2617)
= 2617 – 131
= 2486 km²
After 4 years area of forest = 2486 – (0.05 × 2486)
= 2486 – 124
= 2362 km²
After 5 years area of forest = 2362 – (0.05 × 2362)
= 2362 – 118
= 2244 km²
After 6 years area of forest = 2244 – (0.05 × 2244)
= 2244 – 112
= 2132 km²
After 7 years area of forest = 2132 – (0.05 × 2132)
= 2132 – 107
= 2025 km²
After 8 years area of forest = 2025 – (0.05 × 2025)
= 2025 – 101
= 1924 km²
After 9 years area of forest = 1924 – (0.05 × 1924)
= 1924 – 96
= 1828 km²
After 10 years area of forest = 1828 – (0.05 × 1828)
= 1828 – 91
= 1736 km²
After 11 years area of forest = 1736 – (0.05 × 1736)
= 1736 – 87
= 1650 km²
After 12 years area of forest = 1650 – (0.05 × 1650)
= 1650 – 82
= 1567 km²
SECOND METHOD:
Depreciation formula
`InitialValue{(1-PercentDecrease)}^{TimePeriodInYears}`
Here,
Initial value = 2900 km²
Percent decrease = 5% = `frac{5}{100}` = 0.05
Time period = 12 years
Thus,
Area after 12 years `= 2900{(1-0.05)}^{12}` Solve bracket first
`= 2900(0.95)^{12}` Solve power
`= 2900times0.54036` Multiply
`= 1567.04` km²