Answer :
The Mechanical Engineering Department can afford to spend $12,144.128 on the new energy management system. The selected answer of $189,258 is incorrect. The correct answer is $12,144.128, as calculated below.
To calculate this, we need to consider the present value of the annual cost of the software over the next 5 years, taking into account the effective interest rate of 10% per year.
Step 1: Calculate the present value of the annual cost:
The annual cost of the software is $31,200 per year for the next 5 years.
Using the formula for calculating the present value of an annuity, we can calculate the present value as follows:
PV = C × (1 - (1 + r)^(-n)) / r
Where:
PV = Present value
C = Annual cost
r = Interest rate per period
n = Number of periods
In this case, C = $31,200, r = 10% or 0.10, and n = 5.
Using the formula, we can calculate the present value as follows:
PV = $31,200 × (1 - (1 + 0.10)^(-5)) / 0.10
= $31,200 × (1 - 1.61051) / 0.10
= $31,200 × (-0.61051) / 0.10
= -$19,055.872
Step 2: Calculate the amount the department can afford to spend:
To find the amount the department can afford to spend, we need to add the present value to the cost of the software for the first year:
Amount = PV + C
= -$19,055.872 + $31,200
= $12,144.128
Therefore, the Mechanical Engineering Department can afford to spend $12,144.128 on the new energy management system.
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