Final answer:
To justify the $7500 cost of a high-efficiency motor at a 12% interest rate over 10 years, an annual energy cost savings of $1327 is required.
option a is the correct
Step-by-step explanation:
Calculating Annual Energy Cost Savings
To determine the annual energy cost savings required to justify the expense of a $7500 high-efficiency motor with a lifespan of 10 years and an interest rate of 12%, we need to calculate the annual equivalent cost (AEC) of the motor's expense.
The AEC can be found using the formula for the present value (PV) of an annuity, which is:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
- PMT is the Payment (annual cost savings required)
- r is the annual interest rate (0.12 in this case)
- n is the number of periods (10 years)
Rearranging the annuity formula to solve for PMT gives us:
PMT = PV * r / (1 - (1 + r)^-n)
Substituting the given values:
PMT = $7500 * 0.12 / (1 - (1 + 0.12)^-10)
After calculating, we find that:
PMT = $1327
Therefore, the annual energy cost savings needed to justify the investment in the high-efficiency motor would be $1327.