Ten cavemen with a remaining average life expectancy of 10 years use a path from their cave to a spring some distance away. The path is not easily traveled due to 100 large stones that could be removed. The annual benefit to each individual if the stones were removed is $9.25. Each stone can be removed at a cost of $1.75. The interest rate is 2%. Click here to access the TVM Factor Table Calculator Part a Compute the benefit/cost ratio for the individual if he alone removed the 100 stones.
Ten cavemen with a remaining average life expectancy of 10 years use a path from their cave to a spring some distance away. The path is not easily traveled due to 100 large stones that could be removed. The annual benefit to each individual if the stones were removed is $9.25. Each stone can be removed at a cost of $1.75. The interest rate is 2%. Click here to access the TVM Factor Table Calculator Part a Compute the benefit/cost ratio for the individual if he alone removed the 100 stones.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
 to access the TVM Factor Table Calculator.
#### Part A
**Task:** Compute the benefit/cost ratio for the individual if he alone removed the 100 stones.
**Instructions:**
1. Carry all interim calculations to 5 decimal places.
2. Round your final answer to 2 decimal places.
3. The tolerance is ±0.02.
**Calculation Steps:**
Let’s break down the steps to compute the benefit/cost ratio:
1. **Total Cost of Removing Stones:**
- Cost per stone = $1.75
- Number of stones = 100
- Total Cost = 100 * $1.75
2. **Annual Benefit:**
- Annual Benefit per individual = $9.25
- Number of individuals = 10
3. **Present Value of 10 Years of Benefit:**
- Life expectancy = 10 years
- Annual Benefit = $9.25 / individual
- Interest rate = 2%
4. **Benefit/Cost Ratio Calculation:**
- Compute the total benefit and total cost.
- Compute the present value of the total benefit over 10 years.
- Compute the benefit/cost ratio by dividing the present value of total benefits by the total cost.
**Detailed Explanation:**
1. **Cost Calculation:**
- Total cost = 100 stones * $1.75 = $175.00
2. **Benefit Calculation:**
- Annual benefit per individual = $9.25
- Total annual benefit for 10 individuals = 10 * $9.25 = $92.50
3. **Present Value (PV) of the Benefits:**
- Using the present value of an annuity formula:
\[ PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \]
where:
- \( PMT](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f889cd-13fd-4c48-a7b3-985fea806cfa%2Fc77ffb2f-2406-4a68-ba99-7b62305afc03%2Fbnp8bzp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### TVM Factor Calculation in Caveman Society
**Scenario:** Ten cavemen with a remaining average life expectancy of 10 years use a path from their cave to a spring some distance away. The path is not easily traveled due to 100 large stones that could be removed. The annual benefit to each individual if the stones were removed is $9.25. Each stone can be removed at a cost of $1.75. The interest rate is 2%.
Click [here](#) to access the TVM Factor Table Calculator.
#### Part A
**Task:** Compute the benefit/cost ratio for the individual if he alone removed the 100 stones.
**Instructions:**
1. Carry all interim calculations to 5 decimal places.
2. Round your final answer to 2 decimal places.
3. The tolerance is ±0.02.
**Calculation Steps:**
Let’s break down the steps to compute the benefit/cost ratio:
1. **Total Cost of Removing Stones:**
- Cost per stone = $1.75
- Number of stones = 100
- Total Cost = 100 * $1.75
2. **Annual Benefit:**
- Annual Benefit per individual = $9.25
- Number of individuals = 10
3. **Present Value of 10 Years of Benefit:**
- Life expectancy = 10 years
- Annual Benefit = $9.25 / individual
- Interest rate = 2%
4. **Benefit/Cost Ratio Calculation:**
- Compute the total benefit and total cost.
- Compute the present value of the total benefit over 10 years.
- Compute the benefit/cost ratio by dividing the present value of total benefits by the total cost.
**Detailed Explanation:**
1. **Cost Calculation:**
- Total cost = 100 stones * $1.75 = $175.00
2. **Benefit Calculation:**
- Annual benefit per individual = $9.25
- Total annual benefit for 10 individuals = 10 * $9.25 = $92.50
3. **Present Value (PV) of the Benefits:**
- Using the present value of an annuity formula:
\[ PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \]
where:
- \( PMT
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