Your firm is purchasing a new telephone system, which will last for four years. You can purchase the system for an upfront cost of $$150000,$ or you can lease the system from the manufacturer for $$4000$ paid at the end of each month. Your firm can borrow at an interest rate of $5\%$ APR with semiannual compounding.

Should you purchase the system outright or pay $$4000$ per month?