Roger borrows $$4500$ at $9\%$ simple interest on July $3,1993.$ He pays $$1250$ on October $27,1993,$ and $$2500$ on January $7,1994.$ Find the balance due on May $1,1994,$ using exact time$/$exact interest $($a$)$ by the Merchant's Rule; $($b$)$ by the United State Rule? Ans. $($a$)$ $$957\mathrm{.}50$; $($b$)$ $$965\mathrm{.}08$