Anna borrows $$50,000$ from the bank at a nominal interest rate $i^{(12)}=6\%,($compounded

monthly$).$ She repays this loan by making monthly payments $($at the end of each month$)$

for $6$ years. If each of the first $36$ payments are of $$R$ and each one of the last $36$

payments are of $$(R+1000).$ Using geometric series, determine $R,$ AND the interest

that Anna paid to the bank.