A community recreation centre needs new sound equipment every $18$ months. The manager is looking at these two options:

Buy equipment for $$11200$ on credit at $0\mathrm{.}7\%,$ compounded monthly, for $18$ months. The store selling the equipment guarantees that it will take the equipment back as a trade$-$in for new equipment in $18$ months. The trade$-$in value will be $$5000.$

Lease equipment for $$1000$ down and $$455\mathrm{.}56$ per month for $18$ months.

The recreation centre will recoup some of the cost of the equipment by charging groups that use the centre $$35$ a night. As well, the centre will rent out the equipment an average of $4$ nights a week.

a$)$ What would a lease cost the centre?

b$)$ What would the centre pay to buy the equipment if it makes one payment at the end of $18$ months?

c$)$ How much would the centre earn from renting the equipment over $18$ months? How does this affect the overall cost of each option?

d$)$ What would you advise the manager to do$?$ Explain.