Question

The scrap value of a machine at the end of its useful life is given by S(n)=C(1-r), where C is the original cost, n is the useful life

of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.
Original cost, $41,000; life, 10 years; annual rate of value lost, 13%

Answer 1

$ 2,484.23

Explanation:

The formula for scrap value is

S(n) = C( 1- r)ⁿ

where
S(n) = scrap value after n years
C = original cost
r = rate of value lost in decimal
n = number of years

First convert r to a decimal by dividing by 100

r = 13/100 = 0.13

S(10) = 10,000(1 - 0.13)¹⁰
= 10,000 x (0.87)¹⁰
= 10000 x 0.248423

= $ 2,484.23