Final answer:
To find out how long it will take for a machine that depreciates at a rate of 1.8% per annum to halve in value, we use the exponential decay formula. This involves logarithms to solve for the time given the initial value, the depreciation rate, and the final value.
Step-by-step explanation:
The student's question pertains to determining the duration it will take for a CNC machine that depreciates at a rate of 1.8% per annum to reach half its original value of £100,000, which would be £50,000. To calculate this, we can use the formula for exponential decay, which is:
V = P(1 - r)^t
Where V is the final value, P is the principal amount (£100,000), r is the depreciation rate (1.8% or 0.018), and t is the time in years. We can rearrange the formula to solve for t:
t = ln(V/P) / ln(1 - r)
Plugging in the values, we get:
t = ln(£50,000/£100,000) / ln(1 - 0.018)
Calculating this will give us the number of years it will take for the machine's value to reduce to £50,000 due to depreciation.