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 atthe end of 3 years if the original cost was $1963 and r = 0.2. Round to the nearest cent.

Answer 1

We need to find the value V of a machine, given by:

$V=C(1-r)^t$

where C is the original cost, t is the number of years, and r is the rate of depreciation.

For this problem, we have:

$\begin{gathered} C=\text{ \ }1963 \\ r=0.2 \\ t=3 \end{gathered}$

Then, using the above information in the formula, we obtain:

$\begin{gathered} V=\operatorname{\ }1963(1-0.2)^3 \\ \\ V=\operatorname{\ }1963(0.8)^3 \\ \\ V=\operatorname{\ }1963(0.512) \\ \\ V\cong\operatorname{\ }1005.06 \end{gathered}$

Therefore, rounding to the nearest cent, we obtained:

Answer: $100.06