Answer:
5.1 years
Step-by-step explanation:
the formula for fixed rate depreciation is
Value after t years = initial value ( 1 - r )^t
where r = depreciation rate = 6.25% = 0.0625
t = length of time in years (we are asked to find this
Value after t years = given as $11,500
initial Value = given as $16,000
Substituting this into equation
11,500 = 16,000 (1 - 0.0625) ^t
11,500 = 16,000 (0.9375) ^t (divide both sides by 16,000 and rearrange)
0.9375^t = 11,500 / 16000
0.9375^t = 0.71875 (taking log of both sides)
t log 0.9375 = log 0.71875
t = log 0.71875 / log 0.9375 (use calculator)
t = 5.12
t = 5.1 years (nearest tenth)
