Question

The value of a machine, V, at the end of t years is given by V=C(1−r)^t, where C is the original cost and r is the rate of depreciation. Find the value of a machine at the end of 3 years if the original cost was $1919 and r=0.2. Round to the nearest cent.

Answer 1

The value of the machine after 3 years, with an original cost of $1919 and depreciation rate of 0.2, is $982.08.

Step-by-step explanation:

The value of a machine, V, at the end of t years is given by V=C(1−r)^t, where C is the original cost and r is the rate of depreciation. To find the value of a machine at the end of 3 years with an original cost of $1919 and a depreciation rate of 0.2, we apply the formula:

V = 1919(1 - 0.2)^3

First, calculate 1 - 0.2, which gives us 0.8. Then, raise 0.8 to the power of 3 (0.8^3), which gives us 0.512. Finally, multiplying the original cost ($1919) by 0.512 gives us the depreciated value of the machine after 3 years. So, V = 1919 × 0.512 = $982.08.