Aye wants to repay her $$15,000$ consumer loan from her bank in installments of $$1,000$ at the end of each year for the required number of years. If she has less than $$1,000$ remaining, how many payments will she make and how much will her final payment be if she pays after the last installment? The effective annual interest rate is $\%2.$

Note: please can you do the question according to the formulas given below.