The local parts shop buys a machine that costs $500,000. Its value depreciates exponentially each year by 10%.

Question

What is the machine's value after 5 years? Round your answer to the nearest integer. _________

explain

Answer 1

To calculate the machine's value after 5 years, we can use the formula for exponential depreciation:

V(t) = Initial Value x (1 - r)^t

where:
V(t) = value after t years
Initial Value = $500,000
r = 10% = 0.1
t = 5 years

Plugging in the values:

V(5) = $500,000 x (1 - 0.1)^5
V(5) = $500,000 x (0.9)^5
V(5) = $500,000 x 0.59049
V(5) = $295,245

Therefore, the machine's value after 5 years would be approximately $295,245.

Answer 2

are you sure

Answer 3

Apologies for the confusion earlier. Let's re-calculate it to confirm:

Given:
Initial value = $500,000
Depreciation rate = 10%
Number of years = 5

After 1 year:
Value after 1 year = $500,000 x (1-0.1)
Value after 1 year = $500,000 x 0.9
Value after 1 year = $450,000

After 2 years:
Value after 2 years = $450,000 x 0.9
Value after 2 years = $450,000 x 0.9
Value after 2 years = $405,000

After 3 years:
Value after 3 years = $405,000 x 0.9
Value after 3 years = $405,000 x 0.9
Value after 3 years = $364,500

After 4 years:
Value after 4 years = $364,500 x 0.9
Value after 4 years = $364,500 x 0.9
Value after 4 years = $328,050

After 5 years:
Value after 5 years = $328,050 x 0.9
Value after 5 years = $328,050 x 0.9
Value after 5 years = $295,245 (rounded to the nearest integer)

Therefore, the machine's value after 5 years would actually be approximately $295,245. Thank you for your patience.