Respuesta :
Answer:
The answer is "$38,578, $40,294, choose Machine 2".
Explanation:
Machine 1
Yearly savings = $5,000
Time = 6 years
Rate of Interest = 10%
Calculating the Future value:
[tex]FV = \$ 5,000 ( \frac{F}{A}, i, n)\\\\[/tex]
[tex]= \$ 5,000 (\frac{F}{A}, 10 \%, 6)\\\\= \$ 5,000 \times 7.7156\\\\= \$ 38,578\\\\[/tex]
Machine 1 savings would have a potential value of $38,578
Machine two
Yearly savings = 6,000
Time = five years
Rate of interest = 10%;
At the end of 5 years compute Potential value:
[tex]FV = \$ 6,000 (\frac{F}{A}, i, n) \\\\[/tex]
[tex]= \$ 6,000(\frac{F}{A}, 10 \%, 5)\\\\= \$ 6,000 \times 6.1051\\\\= \$ 36,630.6\\\\[/tex]
At the end of 5 years the potential value is $36,630.6.
The future value in Year 6 calculate-
[tex]FV = \$ 36,630.6 (\frac{F}{P}, i, n)\\\\[/tex]
[tex]= \$ 36,630.6 (\frac{F}{P}, 10 \%, 1)\\\\= \$ 36,630.6 \times 1.100 \\\\= \$ 40,293.66 \ \ or \ \ \$ 40,294\\\\[/tex]
Machine 2 saving will be worth $40,294 in future
Machine 2 's potential saving value is higher.
Thus, You can pick Machine 2.
