A government is considering paving a highway with a newly developed wear-proof material. Paving the highway would cost $4 billion today but would save $400 million in maintenance costs for each of the next ten years. Use the concept of present value to determine whether the project is worth undertaking if the government can borrow at an interest rate of 4%. Is it worth it if the interest rate is 0%? 8%? A politician says to you, I dont care what the interest rate is. The project is clearly a good investment: it more than pays for itself in only 8 years, and all the rest is money in the bank. Whats wrong with this argument, and why does the interest rate matter?

******Answer this portion: Consider the same highway paving project from question 8. A second politician says to you, At an interest rate of 4%, the project is a bad idea. Over 10 years, the project reduces maintenance costs by a total of $4 billion. But borrowing $4 billion for 10 years at a 4% interest rate means paying $1.44 billion in interest. The total cost of the project over 10 years is therefore $5.44 billion! Whats wrong with the second politicians argument?

Please give details to justify answer, thank you.