An internet book distribution company is considering purchasing a sophisticated

Question

An internet book distribution company is considering purchasing a sophisticated computer system to "cube" a book's dimensions -measure its height, length, and width so that the proper box size will be used for shipment. This will save packing material, cardboard, and labor. If the savings will be $12,000 the first year, $13,000 the second, and amounts increasing by $1000 each year for 10 years, what are the (a) present worth and (b) the uniform annual worth of the system at an interest rate of 15% per year?

Explanation / Answer

For present worth, future values are discounted.
Let F be the future value T years from present.

Present value = F/ ( 1 + rate/100)^T

Present worth = 12000/(1.15)^1 + 13000/(1.15)^2 + 14000/(1.15)^3 + 15000/(1.15)^4 +16000/(1.15)^5 + 17000/(1.15)^6 + 18000/(1.15)^7 + 19000/(1.15)^8 + 20000/(1.15)^9 + 21000/(1.15)^10

Present worth = $ 77183

Let uniform annual worth be $" x"

10*x = 77183

x= $ 7718.30

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