2. (10 points) A farm must decide whether or not to purchase a new tractor. The tractor will reduce costs by $2,000 in the first year, $2,500 in the second, and $3,000 in the third and final year of usefulness. The tractor costs $9,000 today, while the above cost savings will be realized at the end of each year.

(a) If the interest rate is 7 percent, what is the present value of the cost savings of purchasing the tractor? Please show your calculations.

(b) Is there any interest rate at which the farmer will decide to buy the tractor. Please explain, without actually calculating present value.