Question

uestion 8 10 points The maintenance costs of a piece of equipment are expected to be S1 500 at the end of the first year and expected to increase by $125 each year through year seven Assuming an interest rate of 10% Match the following questions with the closest correct answers from the given list What is the present worth of base amount? A $1595 D B. 51280 C. 57302 What is the present worth of gradient amount? What is the present worth of maintenance costs? What is the equivalent annual cost? D. $294 E. S435.24 F. $8898 GS1827

Answer 1

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