The narrow gravel road to Johnson Lake is open only for the summer months. At present the county spends $750 per mile each year to prepare the road for summer traffic and another $150 per mile for maintenance during the period in which it is open. A "permanent" road could be constructed at a cost of $10,000 per mile'; the county would have to spend $800 per mile for maintenance only every 5 years through the 30 year life of the road. prospects for the area suggest that the road would have to be relocated at the end of that period. If 8% is reasonable discount rate, which option is less costly? what discount rate would cause the two alternatives to have the same cost in the present value terms. Please show work.