Questions: 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 4 years if the original cost was 2040 and r=0.1. Round to the nearest cent.
Transcript text: 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 4 years if the original cost was $\$ 2040$ and $r=0.1$. Round to the nearest cent.
Solution
Solution Steps
Step 1: Identify the Parameters
The original cost of the machine, $C$, is $2040.
The rate of depreciation, $r$, is 0.1.
The time in years, $t$, is 4 years.
Step 2: Substitute the Parameters into the Formula
The formula to find the value of the machine at the end of $t$ years is $V=C(1-r)^{t}$.
Step 3: Calculate the Depreciation Factor
The depreciation factor, $(1-r)^{t}$, is calculated as $(1-0.1)^{4} = 0.656$.
Step 4: Calculate the Value of the Machine
The value of the machine, $V$, is calculated as $2040 \times 0.656 = $1338.44$.
Final Answer:
The value of the machine at the end of 4 years, rounded to 2 decimal places, is $1338.44.