Lucia Gabrielli purchased an n$-$year par$-$value $$2,000$ bond that had a coupon rate of $9\%$ convertible quarterly; here $4$n is an integer. Her sister Elana purchased a par$-$value bond with an identical coupon rate but having a term of $2$n years. The coupons that Lucia and Elana received for the n years they both held their bonds were identical, and the yield rate used to determine the prices of each of the bonds was a nominal rate of $6\%$ convertible quarterly. Elana paid $$233\mathrm{.}02$ more than Lucia. Calculate the number of coupons in Lucia$$s bond; use the premium$-$discount equation. SHOW WORK, do not use excel sheets, use financial math.