1). Present value of base amount:
We can use the following formula for finding present value of base amount:
(((1+i)^N)-1)/(i*(i+1)^N))*Base amount; where i= interest rate and N is the number of years.
i is given as 10%, N is 7 Years and Base amount is 1500.
On substituting, we have (((1.1^7)-1)/(0.1*(1.1^7))*1500
= $7302
2). Present worth if gradient amount:
we can use the formula:
((((1+i)^N)-(i*N)-1)/((i^2)*(1+i)^N))*Gradient amount
On Substituting, we have (((1.1^7)-(0.1*7)-1)/((0.1^2)*1.1^7))*125
= $1595
3). Present worth of maintenance costs:
This is the sum of both Present worth of base amount and Present worth of gradient amount
= $7302.63+$1595.39= $8898
4). Equivalent annual cost:
Let x be the equivalent annual cost.
Then, x/(1.1)+x/(1.1)^2+x/(1.1)^3+.....x/(1.1)^7= 8898
x((1/1.1)+(1/1.1^2)+(1/1.1^3)+...(1/1.1^7))= 8898
x*4.86= 8898
x= $1827
uestion 8 10 points The maintenance costs of a piece of equipment are expected to be...
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