Question

1. Find the numerical value of the following factor by interpolation
(P/F, 14.75%, 8 )

*Note: Construct Cash flow diagrams for Questions 2-4 and solve them. 1. Find the numerical value of the following factor by interpolation (10 points) (P/F, 14.75%, 8) 2. A cash flow sequence starts in year 1 at $9000 and decreases by $250 each year through year 12. (a) Determine the value of the gradient G; (b) determine the amount of cash flow at the end of year 8; and (c) determine the value of n for the gradient. (20 points) 3. Amazon 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 $175,000 the first year, $185,000 the second year, and amounts increasing by $10,000 each year through year 9th , what is the total present worth of the system at an interest rate of 10% per year? (35 points) 4. Chemical costs associated with a packed bed flue gas incinerator (for odor control) have been decreasing uniformly for 5 years because of increases in efficiency. If the cost in year 1 was $100,000 and it decreased by $5000 per year through year 5, calculate the present worth of the costs at 10% interest rate per year? (35 points) Fluidizing bed incinerator

2. A cash flow sequence starts in year 1 at $9000 and decreases by $250 each year through year 12. (a) Determine the value of the gradient G; (b) determine the amount of cash flow at the end of year 8; and (c) determine the value of n for the gradient.

3. Amazon 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 $175,000 the first year, $185,000 the second year, and amounts increasing by $10,000 each year through year 9th , what is the total present worth of the system at an interest rate of 10% per year?

4. Chemical costs associated with a packed bed flue gas incinerator (for odor control) have been decreasing uniformly for 5 years because of increases in efficiency. If the cost in year 1 was $100,000 and it decreased by $5000 per year through year 5, calculate the present worth of the costs at 10% interest rate per year?

Answer 1

1. Let (P/F, 14.75%,8) = n

When, i = 14% , value of (P/F, 14%,8) = 0.350559

When, i = 15% , value of (P/F, 14%,8) = 0.326902

using interpolation

14.75% = 14% + (0.350559 - n) / (0.350559 - 0.326902) *(15% - 14%)

0.75 = (0.350559 - n) / (0.350559 - 0.326902)

0.75 = (0.350559 - n) / 0.023657

n = 0.350559 - 0.023657 * 0.75 = 0.332816

(P/F, 14.75%,8) =  0.332816

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