Question

A factory machine was purchased for $45,000 and has an estimated lifetime of 8 years. If the
scrap value (Resale) at the end of 8 years is estimated at $3000. (4 Marks)
a. find the book value function V=f(t).
b. Find value of machine after 3.5 years and 7 years.
c. Sketch Book Value function.

Answer 1

Given : A factory machine was purchased for $45,000 and has an estimated lifetime of 8 years. If the scrap value (Resale) at the end of 8 years is estimated at $3000.

To Find :  

a. find the book value function V=f(t).

b. Find value of machine after 3.5 years and 7 years.

c. Sketch Book Value function.​

Solution:

Initial Value = 45000

Final Value =  3000

rate of depreciation = r

t = Time period = 8 years

A = P ( 1 - r/100)^t    ( -ve sign shows depreciation )

=> 3000 = 45000 (1  - r/100)⁸

=> 1/15 =  (1  - r/100)⁸

=> 0.712834 = 1 - r/100

=> r = 28.71657 %

V = f(t)  =  45000 (0.712834)^t

Substitute value of t :

Value after 3.5 years = 13,761.7

Value after 7 years   = 4,208.5

Learn More:

calculate the compound interest for the second year on rupees 8000 ...

brainly.in/question/17821541

compound interest on a certain sum of money is ₹ 12960 in third ...

brainly.in/question/19026958