Equipment maintenance costs for manufacturing explosion-proof pressure switches are projected to be $125,000 in year 1 and increase by 4% each year through year 5. What is the equivalent uniform annual worth of the maintenance costs at an interest rate of 10% per year, compounded semiannually

The equivalent uniform annual worth of the maintenance costs at an interest rate of 10% per year, compounded semiannually is $127,432

Explanation:

In order to calculate the equivalent uniform annual worth of the maintenance costs at an interest rate of 10% per year, compounded semiannually we would have to calculate the following formula:

equivalent uniform annual worth of the maintenance costs= P(i(1+i)∧n/(1+i)∧n-1

The rate of interest i would be as follows:

rate of interest i=(1+10%/2)-1

rate of interest i=0.1025*100

rate of interest i=10.25%

The present value P would be calculated as follows:

present value P=$125,000(1-(1+1/100)∧5 (1+10.25/100)∧-5/(10.25/100-1/100)

present value P=$125,000*3.84

present value P=$480,000

Therefore,

equivalent uniform annual worth of the maintenance costs=$480,000*(10.25/100 (1+10.25/100)∧5/(1+10.25/100)∧5-1)

equivalent uniform annual worth of the maintenance costs=$480,000*0.2654

equivalent uniform annual worth of the maintenance costs=$127,432

The equivalent uniform annual worth of the maintenance costs at an interest rate of 10% per year, compounded semiannually is $127,432