Lucia Gabrielli purchased an n-year par-value $2000 bond that had a coupon rate of 9% convertible quarterly; here 4n is an integer. Her sister Elana purchased a par-value bond with an identical coupon rate but having a term of 2n years. The coupons that Lucia and Elana received for the n years they both held theirs bonds were identical, and yield rate used to determine the prices of each of the bonds was a nominal rate of 6% convertible quarterly. Elana paid $233.02 more than Lucia. 

Calculate the number of coupons in Lucia's bond; use the premium discount equation.