Question

A CNC machine centre costs £100,000. Its value depreciates at X% per annum.

(a) What will be its value after Y years?

(b) How long will it take to have a value of £50,000?

Answer 1

a)

value after 1 year:

$100000-100000x=100000(1-x)$

after 2 years:

$100000(1-x)-100000(1-x)x=100000(1-x)(1-x)$

after y years:

$100000(1-x)^y$

b)

$100000(1-x)^y=50000$

$y=\frac{1}{2ln(1-x)}$